With a 60A fuse you have no real issues with a typical cooker, most domestic ones are fine on a 32A breaker as they rarely are all on max for any length of time and thus the typical diversity allows that even for ones that are of the order of 11.5kW = 50A (formula is 10A plus 30% of remainder so 10 + 0.3 * (50- 10) = 22A).
It is not very tidy but at least you have the isolator so rest of electrics can be sorted now. And you really should!
That board is probably pre-1970 and looks like single 30A circuit for sockets (fairly common for a flat), 5A for lights (electrically OK as rarely much power demand but practical/safety better with two so in the event of a fault you have some lights still working), and a 30A cooker. You don't really need that many circuits but think about anything you want added and at the very least get the sparky to fit one with a couple of spare ways for anything in the future.
If you have just moved in then think about if it needs a rewire. The existing cable might be OK (PVC if not abused by overheating, rodents, or exposure to sunlight will last many decades) and some inspection and insulation testing would determine that, but given the apparent age there are unlikely to be enough sockets or lights in each room or where you want them to be.
Yes, it is a non-trivial expense but if needed at all then best to do before you spend much on decorating, etc.