The bike probably will work on 36V. You have to look at your LCD setup instructions. If it allows for 36V, you probably can change the battery. Setup is very critical, because you need the system to use the proper low voltage cutoff for the higher voltage battery. Otherwise, you could damage the battery and increase the risk of a fire,
Also look at the specs on the controller, inside the plastic box on your seat tube. If it only allows 24V, then you do have to replace it,
Worst case, you buy a new controller/LCD. They're about $100 USD from China, so whatever that costs in your country, which I assume is the UK. I suppose you know what a battery will cost.