The same thing happened with my Elan (dual Strombergs) a few months ago. I'm not exactly sure what the problem was, but it seemed like the jet on one carb was partially blocked.
Silly enough, the way I fixed it was to put both hands over each carb intake while the engine was running. That created a ton of extra vacuum that couldn't suck air in, so it of course killed the car. However, next time I started it up, the problem was gone. Probably not the "technically correct" solution, but somewhat supports my theory as to the blocked yet.
Does the TR7 choke both carbs, or just one? My Elan only has the choke on the front carb, so it was easy to determine which carb was causing the problem.
I know, I'm mostly rambling, but I hope that helps a little.