When a car won't start, I like to first think simple. For me, it's almost always: 1) gas; 2) ignition; or 3) battery. In colder weather, a good old British car sometimes needs a firm pull of the choke. For me, I pull it nearly all the way out to start.
I can't tell from your case, but:
First, be absolutely certain that your choke linkage is working and "holding." In some cars you have to hold the choke until the car warms up. Verify that when the choke is pulled, it's doing its job at the carburetors, not just taking up slack.
Then, don't guess that your fuel pump is working or that your fuel line is clear. Verify that so you don't waste time. I can't tell you the time I once wasted before I learned of an obstruction in my fuel line. You might want to pull your fuel line off the carbs and hold a can to catch the fuel while someone turns the key--or some other quick approach. Gas flow show be strong and consistent with the cranking of the engine.
If neither choke nor gas is the problem, be sure that the ignition is sending current to the coil and that the wiring from the ignition to the coil is not corroded or broken. Last year, my car was starting "off and on." To my surprise, the wiring to the coil was so corroded at the slide connector to the coil that the current was only intermittent. That seemed like a freak occurrence, but it was sure easy to fix once I discovered that with just a wiggle of a wire, no current was reaching the spark plugs. I fixed the connection and the car immediately started.
If the problem clearly is not the choke, nor the fuel system, nor the spark/coil/ignition, and if the car actually does start sometime, as you indicate, it's possible that you have the timing materially off the mark. I wouldn't underestimate that possibility. When my timing is on the mark, the car starts up easily. Unfortunately, I have a trade off--I retard the timing for better performance, and suffer a bit on ease of start up. I'm working on that.
Finally, and maybe as important as anything (and like another has advised), it's possible your points are totally fried or way off the right gap. Of course, check that.
Anyway, I'm no pro. Advice here is from a trial and error do-it-yourself LBC owner who has been stuck about everywhere, tried about everything, been splashed in a good suit with gas, grease and coolant, and somehow never had to tow an LBC anywhere.
Good luck.