Just to save time later, try the old trick of putting the car in 4th gear,
rolling backwards and forwards a few times to turn the engine, and then try a
restart. Every so often, the starter will get stuck on the ring gear,
effectively grounding it out.
If THAT doesn't work...
1) Double-check your battery: fluid level first, then use a multimeter to
check the charge. It may be lower than you think.
2) Just for fun, make sure the coil wire (high tension) is connected, and
that the coil is properly grounded.
3) Run a jumper wire from the + terminal of your battery directly to the
starter solenoid (heavy guage, please, and do NOT touch the body with the hot
end of the jumper). Safest way to do this is to run it from the solenoid end
first, then back to the battery. If the car tries to turn over, your problem
is somewhere in between (brainbox for your elec ignition, relay, etc.). If
the car does not try to turn over, then the problem is likely in the starter
itself (assuming 0-2 above yield no solution).
In general, the trick to solving electrical/starting problems is to trace the
circuit, identify the elements in the circuit, and then sort through this
list to see which subsystems can be isolated as cause/not cause of the
75 MGB 'Rags'