If I theoretically decide to sell my car and buy another several times during the year, just how many times could I do this before the insurer turned round and refused cover?

I don't see a problem with this so long as I'm paying the right amount for cover, and paying any admin fees if they ask.

What's the most number of times anyone has changed their car during the year?

 

Depending on the insurer several times will be exceptable, unless
you are a motor trader and thats where some companies will start
asking more questions or refuse cover.

When you start a policy explain to the ins co or broker that you are likley to change cars quite often, for what ever reason it is
i.e you get bored easy. If your upfront with them there should'nt
be a prob.

simb