I know very little about any of the hotels mentioned, but if you want a proper pool that's what I would focus on in picking the hotel. That's easier to search for photo-wise.

If you're serious about spinning, how about using a pay-as-you-go gym/class instead? There are loads of great gyms all over London for this. For example literally right opposite the Mondrian is 1Rebel which has excellent spin (Ride) classes (the Reshape class is also great). You could get a trial membership on Classpass for your trip for these.