I can confirm you can swap out a halogen hob for a 13 amp appliance (eg induction hob), however from my experience the hob will be under-powered, when it comes to boiling up water on multiple zones. However some hobs have a boost function which can put all the power into one zone to get it up to temp, which overcomes the lack of power.
Some induction hobs can also be limited down in the settings as part of install, so you could buy a 25A induction hob but configure it to run at 15 or 20A, however again this is a feature of the hob and not all hobs support this option, and you would need to speak with the sales team as to what hobs have this function.
When working out the max load, we can assume the oven is around 3KW, and the induction around 7KW, in all installations I have seen a separate feed has been run to the induction hob, which would be a 6mm twin and earth with a 32A breaker.
Please let me know if I can be of any further assistance.