[Kymmy]

Yes the council tax should be in your name as the single person discount will be void.

As for Gas/Electric it's upto you.. The good thing about having it in your own name is that if there's any issues then you can contact them directly.. Also you can change suppliers as costs change..

For the boiler.. it's a fixture of the house and as such he should be responsible for it.. that includes any service contracts on it...but it is entirely upto you if you wish to take it on as again with your b-i-l out of the country contact with the service agents might be problematic unless you pretend to be him.. I'd suggest moving it to your name but negotiating a rent discount to that amount.

One other point is that the more stuff you have in your name the better it is in securing a decent credit history..