Hi Randy,
It sounds like you have your heart set on installing Webers and I wouldn't want to discourage you in any way. In fact, there seem to be more suppliers for Weber parts there in England than here in the U.S.
I suggest you start by getting a book or two on Webers, to become more familiar with their operation and installation, before making your final decision. In fact, a Haynes Techbook Weber Carb Manual I've got also covers SU & ZS carbs, so is a great reference for most any carb likely to end up on a TR4.
Once you have a book or two, you'll find that 42DCOE "Series 8" were what was specified for TR4 back in the day. The reason this size was chosen by the factory for their racing program initially was simple, they were cheap. They also happened to be a good choice of size. The reason they were cheap is that a large auto maker in Italy ordered a huge lot for a production run, then cancelled their order after Weber had already made most of them up. Weber had a fire sale and a lot were installed on the TR 4 cyl. motor. The books also list the "starting point" for venturi and jetting setup on the TR 4 cyl.
42DCOE are no longer made. Haven't been for 10 or more years, I would guess. They were more limited in terms of parts to begin with and parts for them are much more difficult to find now. For example, 42DCOE only had main venturi (chokes) available in even numbered sizes with the largest being 34mm. 40DCOE have a much wider selection in 1mm increments, and go up to 36mm.
In your car you will likely want 32 to 34mm size, depending upon several factors, which would actually allow either size to be used. If you do track down 42DCOE Series 8, be prepared to spend a lot more for a set of chokes, though, simply due to rarity of the parts. As far as I know, only one series of 42s were ever made: the Series 8 I already mentioned.
In addition, you'll want 4.5mm secondary venturi. There are two types of these for 40DCOE carbs. One is longer and sits flush with the front of the carb, is for use without air horns or with surface mount air horns. The other is shorter, stops an inch or so inside the throat and is for use with the longer style of air horns only.
Air horns or ram stacks are a hotly discussed Weber accessory. Basically, they help air flow to be steadier and more consistent, and can help prevent "stand off" where the air fuel mixture is actually pulled back out of the throat of the carb. However, there's a lot of talk about air horns' real value when mounted underneath an air filter on a street car. I figure they can't hurt, have 40-45mm horns on my car (which require deeper air cleaners, I'm using 3" K&N). One consideration, longer air horns are better for low end torque. Shorter ones and really large diameter, full radius ones are more for top end performance. I think TeriAnn talks about these a bit on her site.
I don't believe there were actually more than a few TR4s out of the factory with Webers fitted. In fact, I only know for certain of the Rally Team cars, and those would have been setup initially by the factory racing dept. in England. Here in the U.S., the Kastner/factory prep used modified SUs on TR4 track cars during the peak years of the cars in the early 60s. Webers weren't permitted on Production Class cars initially.
The Rally Team TR4s, with Webers and other mods already in place, were shipped to North America to compete in the Shell 4000 Rally around 1964-65, and Kastner was recruited to prep them. So at least by then he must have been working with the carbs. (This was also the time when he installed American Racing Silverstone wheels - pre-cursors to the now more well-known Minilites - on those cars for the first time, over the initial objections of the rally tech inspectors who felt the mags wouldn't be strong enough and might be dangerous. Just the opposite proved to be true, so the Silverstones found their way from the U.S. racing scene to the UK/European rally circuit.)
Kastner and many others picked up on using Weber DCOE in many race applications, where permitted by the rule book. This is probably enough history, though!
As to your application, you will probably want 40DCOE for street use. These maintain higher intake gas speeds due to the smaller diameter throat, which is good for lower to mid-rpm work. Racers usually use 45DCOE, which can be tuned better for max. rpm operation and will give max HP at the top end, but at the cost of low to mid-range torque and performance.
I agree that to get the best out of them any DCOE should be part of a matched package of engine mods that include a hotter cam, increased compression, freer-flowing exhaust and head work to improve engine breathing. You would find only incremental improvement installing them on an otherwise stock engine. The improvement you see will be due largely to DCOE having an accelerator pump, which both SU and ZS lack. The flip side of this is that the accelerator pump is also the reason Webers can and will consume more fuel. When I floored the pedal, I swear I could see the gas gauge needle moving on my TR4, even with relatively choked down 40DCOE at higher altitudes. It sounded very cool though... and got up and galloped pretty well in spite of my shade tree tuning.
There are many, many different versions of 40DCOE, so be careful shopping. The main designation is an additional number, such as the 40DCOE Series "18" on my car. It's important that the carbs you buy are a matched set, both with the same series number. It's also important that the serial numbers - which are stamped right below the model designation with its series suffix number - be reasonably close, since a much later manufactured carb might have some variations that were implemented during production. The serial numbers are highly unlikely to be exactly sequential, but shouldn't be too far apart. For example, the 40DCOE on my car have serial numbers 151XX and 157XX. I happen to know they were purchased or installed as a set when new, so am satisfied they are a matched set. I'd worry if the serial numbers were wildly different.
There are a wide number of variances within any particular model designation. In the 40DCOE the manual I have lists Series 2, 4, 24, 27, 28, 32, 33, 15/16, 18, 22/23, 29/30, 31, 34/35, 44/46, 76/77, 72/72 and 81. Still being manufactured, there are even more variances today, with Series numbers now in the triple digits.
However, I lucked out back in the 70s when I bought the 40DCOE "8"s still on my TR4. Some key differences between the Series are accelerator pump stroke and float level dimensions, effecting how much fuel is on hand in the carburetor and how much is delivered during acceleration. Now it so happens that 40DCOE 18 have the same accelerator pump stroke (10mm) as the 42DCOE 8 that were original specified for the TR 4 cyl. (Note, the same carbs and basic setup jetting were specified for the engine in 83mm/2 liter and 86mm/2.1 liter form, so there is some flexibility).
The float stroke is slighly shorter, 6.5mm instead of 8.5mm that's on the 42DCOE 8, but I've never noticed any fuel starvation problems.
40DCOE Series 18, 22/23, 29/30 all share the same accelerator pump stroke as 42DCOE8. But, 40DCOE 29/30 have a shorter float stroke (and a lower open position). 40DCOE 22/23 have the same as 40DCOE18 and might be a better choice. On the other hand, 40DCOE 18 were widely used on some production cars and are pretty common.
Speaking of the accelerator pump stroke, a slightly shorter actually wouldn't hurt. But the 10mm found on the carbs I've mentioned is the shortest that was used on the older DCOE (I don't know if newer ones might be offerred with a shorter stroke). Some cars tend get overly rich during the initial acceleration phase, but it's easy to modify the accelerator pump stroke/volume by putting a washer the right size inside it (I didn't find it necessary on my car, but Kastner discusses often needing to do this in his chapters on Weber tuning).
You ask about manifolds and there are a number of different ones to choose. Shop around. I have a Warneford on my car, which I like because it's a one-piece design that fits very well. Most Weber manifolds are two-piece. Unfortunately, I don't think Warneford are still being made and don't know of anyone who is making a similar design. (On the other hand, once installed properly, I suppose a little aluminum welding might convert a two-piece manifold design into a one-piece!)
Other considerations:
Try to locate a local or at least England-based Weber tuner and parts house. This will make tracking down parts much easier and there is no sense in paying double duty on items shipped from the U.S. Plus, it's highly useful to have initial tuning done properly on a dyno (rolling road on your side of the pond). Better yet, if you choose to work with someone like Revington TR, Racetorations or Cambridge Motorsports, they will be quite familiar with Weber setup on TR4 specifically and can probably more quickly get you up and running.
Also check local laws that might effect using Weber DCOE on the street. They are illegal here in California, and I'd most certainly never encourage anyone to do anything illegal! (Note: some Weber downdraft are approved for use in Calif., but those are essentially economy carbs, not very performance oriented. For convience, they can be found on Jeeps, though!) I will tell you that my Weber setup (thanks in part to the one-piece manifold) can be quite easily be completely swapped out in about 15 minutes - for a pre-tuned SU setup I've also got on hand - should I ever need to comply with the rules of the road.
Keep looking for that two-piece Triumph hard top, eventually you will find one! It took me a year or two to finally track one down at a price I could live with (immediately after which I saw another one offered even cheaper on eBay and came very close to having two of them!)
Cheers!