In my borough (Barking and Dagenham in the Met) we have a new unit of officers who are more community geared, back to the old Bobby on the Beat I think, and some of these folks have push bikes. Personally I'd rather not have a bike unless it's got at least a 600cc engine!

But the aforementioned officers don't respond to call's but they do work more closely with the communities and school's.
Actually, thinking about it, I remember when I was a kid we had a copper on a push bike so this isn't anything new, it's re hashing an old idea.