The most common condition in MG dizzys is a frozen mechanical advance. Like "Stewart" said about the points plate, it's probably all gummed up too. Remove the distributor cap take hold of the rotor and Gently wiggle it back and forth. It should move freely a few degrees in the clockwise direction and retun on its own. If it dosen't then the advance mechanism is frozen. If you remove the rotor, then you will see either a small disc of felt or a slotted screw in the top of the distributor shaft. This is supposed to receive a few drops of oil at regular intervals (i.e. every oil change) to keep it free. But it is often neglected and it dosen't take long to quit working.
.The mechanical advance is the system of weights and springs on the distributor shaft down beneath the points plate.Usually it can easily be dismantled and repaired (refer to a service manual)and with the proper care you won't ever have that problem again.
You can check the vacuume advance by removing the dist. cap and seeing if the actuator rod and points plate moves when vacuume is applied to the port. That is a common problem as well.