We need some more information on your car and the circumstances before offering suggestions ...
Any modifications to your car (ignition, fuel, carbs, cylinder head, etc) from a standard '77 B? Does the engine response vary when it's just fired up (below normal temp) or only when at temp? Will it "cut out" only under load, or if rev'ed to higher rpms in neutral while parked? Try to describe what it sounds like when it "cuts out" - backfire? Does it run "rough" above a certain rpm? Problems when accelerating, or if steady speed, or coasting?
Also, details on last tuneup, age of ignition components, fuel filters, any recent work on fuel or ignition parts, etc.
Check out John Twist's MG web site at University Motors http://www.universitymotorsltd.com/.
Lots of Q and A on all models of MGs and how to solve assorted problems.
Repost with as much detail as you can. Good luck!