A Morgan of that age probably has a voltage stabiliser unit. This is supposed to suppress voltage fluctuations and stabilise the fuel gauge reading.
See item 27 here.
http://www.mgocspares.com/acatalog/mgb_instruments.html#a3189W_2d128484

A solution is offered here......
http://www.britishv8.org/Articles/MGB-Voltage-Stabilizer.htm

Look behind the dash, and if you can locate it, try a replacement.

Having said that, this problem persisted on my MGB even with a new unit, and everything else replaced, and I learned to live with it!

DaveW
'05 Red Roadster S1
'16 Yellow (Not the only) Narrow AR GDI Plus 4