Hi,
Sorry to hear about your Father-in-Law.
It might be worth finding out if the local authority where your FIL lived offers a service called "Tell Us Once" - we used this when my FIL and MIL passed away and you can do it at the same time as you register the death. Not all councils are signed up to it but if they are it makes things a lot easier.
They ask for all the relevant details and then pass that on to people like the DVLA, Inland Revenue, TV Licensing,social services, the Dept of Work and Pensions etc. so they all get told at the same time, so it saves you making numerous phone calls and sending out loads of copies of the death certificate. It only works for Govt departments though, you still have to do all the faffing with utilities and banks etc.
Hope all goes well and thinking of you all at this difficult time.