Missing at high speed is often related to fuel starvation or sometimes, weak ignition.
Always look at the cheap and easy things first:
See if your gas cap is properly vented (modern cars have non-vented caps)....if you've got the wrong cap, the fuel pump will have to work against a vacuum after running for a while. Loosen the cap and run the car. If it runs better when loose, you've solved the problem.
Change your fuel filter(s). You may have two...one near the tank and one near the carb.
Remove the top of the carb float chamber (if you have an SU HS-type carb) and clean it out. While you're at it, remove the piston chamber and use low pressure air to blow back through the main jet discharge (this is the hole the tapered piston needle goes into). Do this while the float chamber is apart (this allows any junk to be blown out).
Start the car in a very dark place at night and let it idle. Get a plant mister or spray bottle filled with plain water and mist it all over the engine. This won't hurt anything but it will reveal weak ignition insulation. If you see sparks jumping, you've located an area where the igniton isulation is weak (maybe the plug wire, cap or coil).
There are many more things that could cause your problem, but the stuff above is cheap or free and fairly easy to do.