Hi David,
You didn't say if this noise started occuring recently or if there has just been some work was done on or around the front brakes/wheels/hubs. That would be a clue if the noise is new, and appeared after some parts were installed or some work done.
Disk brake pads do tend to drag lightly against the rotor, even when no pressure is applied to the brake pedal. This is by design and typical of most disk brake setups. It helps keep the rotor clean and dry.
The problem could be as simple as the type of friction material used on the disk brake pads. Are they new? Some materials just make a little noise at startup and, perhaps, just as the car comes to a full stop. This might be a squeek, or a sort of "groaning" noise. Usually it's the "heavy duty" semi-metallic pads that are more inclined to make noise, but this isn't any sort of hard and fast rule. There are alot of different manufacturers and types of pad materials.
A fresh set of pads can take a while to bed in, too, especially if installed on a set of rotors that have some wear and tear. Brand new pads (and new rotors) need to be broken in properly for best operation. This varies a bit from manufacture to manufacturer, but usually means driving at about 35 mph and then applying the brakes smoothly and not too firmly, down to about 5 mph, then releasing for about 30 seconds to let them cool while accelerating back up to 35 mph, then repeating the process 3 or 4 times. Then, do it again but from 50 mph, also repeated a few times. Finally, do it all again several times from about 65 mph.
Using brakes too hard before they are bedded-in can cause a sort of hardened surface to form on the pads, that might tend to make noise and probably won't give full, 100% braking action.
Many mechanics will test drive and bed in the brakes after working on them, before returning the car to the owner. Check with your mechanic, though, to be sure if that's been done, to find out what the manufacturer of the pads they installed recommends and if you need to bed in the brakes yourself.
Actually I think the anti-rattle "shims" seen at the TRF link
https://www.zeni.net/trf/TR6-250GC/101.php in the previous post, should already be installed on your car. As far as I know, these are standard fitment on all TRs. They have to be installed right way around too, the arrow on the shim needs to point toward the front of the car. If these shims aren't in there and properly oriented, the brakes will likely make noises.
There are also greases, gasket-sealer-like material and even stick-on pads that can be used on the back of the pads and shims. Practically any auto parts store has an assortment of these products. However, I personally only use these as a last resort or if specified by the service manual. First see if the shims are in place and properly oriented, and if the retaining pins were replaced with new the last time the brakes were rebuilt (and possibly try a second set of pads). The pins are TRF part # RFK605. They should also have a light coating of grease or anti-seize to help them slide smoothly in the holes in the caliper.
Are you by any chance using DOT 5 brake fluid? I've heard that it doesn't provide as much lubrication within the hydraulic system as DOT3 & 4 and that in some instances some cars have had problems with drag or sticking moving parts, possibly including the pistons in the calipers. I've not specifically heard of this problem on TRs, though.
Were the calipers recently rebuilt? If so, were the pistons replaced? Original pistons had a hard, chrome-like coating that eventually flakes and can cause problems like sticking and damaged seals that cause leaks. Personally, I'd always change to stainless steel caliper pistons, which are available from various vendors.
Another outside possibility: Yours is a late TR6 and surely came originally with the metric-size bolts mounting the calipers fitted. Have the calipers ever been replaced with rebuilt units? If so, they need to be checked that the caliper model matches the type of bolts being used. If I remember correctly, on your car should be Girling 16PB calipers, not 16P that were used on earlier cars.
Also, the pads used on TRs changed slightly at some point. They had different size holes for the mounting pins, but were otherwise pretty much the same. I don't recall which was which, or when exactly the change occured, but I woud suppose it's possible if the wrong pad were used with a caliper, that might cause some rattling or other noise problems.
Another thing to check is the adjustment of the front wheel bearings. If the front hubs have had the grease seals replaced recently, the adjustment might be too loose. The reason for this is that the seals most are selling today are thicker than the originals, which can fool anyone setting the bearing adjustment in the traditional way (i.e. the method outlined in the service manual). Now, I've not specifically heard of the sort of symptoms you describe as a result of this, usually it's that the pads and pistons get knocked too far back into the caliper, due to play in the wheel bearings. This is sort of the opposite of what you describe, and is noticible when the brake pedal goes nearly to the floor without any result, first time the brakes are used after driving for a bit. A quick pump of the brakes will bring them back (repositioning the pads and pistons), but it can be a surprise! I think this unlikely, in your case, but it's important to check.
Lastly, as mentioned, besides the brakes there are other things that might make a sort of squeeking noise. The clutch disk and throwout bearing sometimes chatter or squeek when first released at a standing start. This could be due to a variety of factors, just mentioning it because it might be mistaken for a brake noise.
I agree that noises which appear more from under or toward the rear of the car might be actually be coming from u-joints (there are six on your IRS car) or the sliding sections of drive shaft and axles, which can stick and make noises too if worn and/or lacking lubrication.
Hope this gives you some ideas.