If you have gas to the carb then you probably have a problem inside the carburetor. The float/needle may be stuck closed. It may be time for a rebuild.
Make sure the pistons are free and have 3 in 1 oil in the resovoirs. If the carbs have never been professionally rebuilt, the needle may have been adjusted wrong and rubbing on the side of the jet. You may need to try and buy a rebuild kit for the carbs.
Looking for a Used MGB in your area?
CarGurus has 86 nationwide MGB listings and the tools to find you a great deal.
Search MG MGB Questions
MG MGB Experts
Related Models For Sale