you will probably need the main earth bonds changed to a larger size, which is probably easy. You may have a lack of green/yellow sheathing in switches, sockets and light fittings, which is tedious, and you might take opportunity of changing to new ones. If you are unlucky (but 1980's should be OK) there might be lack of earth wire in lighting, which at the very least means all fittings must be plastic, no metal.
Your cables will be PVC T&E and serviceable unless they have been overheated in lights or by hot pipes.
You probably have insufficient sockets, which is not a fail, but if you are using adaptors (grrrrr) or extensions, you should add more.
You may have bodged alterations or additions. You may have cracked or damaged sockets which is easy.
Flats can be difficult if cables are inaccessible in concrete floors and ceilings.
You are under no obligation to rewire the flat to modern standards, e.g. height of sockets and switches above the floor, though the modern standards are better if you ever plan to be pregnant, fat, disabled or have a bad back.