I can't lie - I'm jealous! Both at the fact that you have a house in London but also a garden that you can build a studio in.
Then I checked your profile n saw you're a veterinary surgeon - nah you can keep that
All the best for it, I'll be interested to hear your solution for the underfloor heating. I've found a suitable studio property in West Midlands where I live but it straddles the top 2 flood risk zones n being that it's close to a railway I'd need to float the floor. Having to budget for flooding with a floating floor plus underfloor heating I think I could blow my whole budget on just that!