The first thing you need to find out is what the Wattage of the oven is. This will determine the size of cable and the “fuse” that is required to protect it.
As stated, many ovens these days are suitable for either a 13A socket or fused spur.
The switch you have which is controlling that oven looks to be a 13A fused spur. You can check this by removing the fuse in the holder to the left of the switch.
You should also go to your consumer unit and find out which “fuse” disconnects that circuit. My guess is that it’s probably a spur off the kitchen ring but you need to confirm this. Assuming that the consumer unit is properly configured then the “fuse” will likely be no more than 32A.
Also, can you determine the size of the cable from the switch to the oven? It’s usually marked on it somewhere.
If you can get some of this info. it might help confirm things but my guess from what I’m seeing here is that provided the new oven is no more than 3kW then the circuit and cabling will be satisfactory.
Double ovens and electric hobs are generally much more power hungry and will require a more robust cable and isolator. If you’re keeping the gas hob and it’s a single oven then I reckon it will be less than 3kW.
Rich.