The differences are largely irrelevant as far as learning to fly goes. They're both pretty good trainers. The C152 can cruise & climb a bit faster but in UK temperatures a C150 will still be quite OK.
A C150 can usually be landed in a shorter distance than a C152 thanks to the 40 deg flap setting. Not that it matters - it's a technique & judgement that you need to learn, something that will be a base to adapt to other types in your future. Just remember to get the flap retracted for go-arounds. Not that the procedure is any different in a C152. Just one fewer stages of flap to retract.
Depending on the year model there were some cabin width gains from early to late model C150s. Don't think there were changes from late model C150s to c152s. Might be a consideration if you're both hefty types.
They're both docile enough for confidence, and they both can be pushed enough to force good technique or get bitten.
You're the customer. Go with the cheapest ie the C150, as long as the useful load is adequate for you, the instructor & sufficient fuel. You can always fly the C152 for navigation exercises for the slight extra useful load & speed. The difference in handling just isn't big enough to worry about.