I was executor for my mother's estate six months ago. I second much of what Galaxymum has said.
Who registered the death? When we went along we took her birth cert, passport, the will, etc and the registrar runs a 'Tell us Once' service, which notified quite a few of the official organisations - Council tax, passport and pensions were automatically cancelled, for instance. it made a bit less work to do.
If your Gran's assets are under a certain limit - I think possibly 15 thousand - you don't need probate, which hastens things along a bit. You'll need advice from the bank for the exact limits - we only needed a solicitor to witness one signature, which he charged a fiver for (cash in hand and from thence to pocket, I suspect).
The utilities varied widely in their competence when I phoned to register the death. I started giving them points out of 10 for competence/friendliness/sensitivity as a way of relieving the frustration. The electricity company were brill, the insurers were shite - some teenager on the phone who couldn't be arsed to even say 'sorry for your loss'. The best companies have dedicated departments to deal with estates and final bills. I had ordered five certified copies of the death cert, and in the end only the bloody insurers asked for it (and it wasn't even life insurance - just house contents!) to keep - everywhere else wanted to see the original but then cave it back.
The one thing I haven't quite been able to face yet is cashing in the 60 quids' worth of premium bonds - they're making a huge fuss about being sent the original will by post, and the risk of it getting lost is too great for a mere 60 quid. It has to be done within a year of the death, and in the end I'll probably do it on the offchance that the bonds have actually won something in the meantime.
It's not great fun, but do allow yourself a few treats while getting through it - I hope your Gran left you a small something for a meal out or a few nice bottles of wine in acknowledgement of all the work involved.
Administering an estate can be daunting, especially for a first time executor or executrix. It doesn't have to be however as long as one knows the general process and some of the terminology. In fact, most of the work (if not all) can be done without having to hire an attorney. Probating the will, issuance of the "Letters Testamentary", obtaining the death certificate, notifying beneficiaries, distributing assets, selling stock can be done by the executor directly.
I was a first time executor for my mothers estate and it was tough. There were a lot of pitfalls but I felt better about doing the work myself rather than handing it over to someone else.
I actually authored and published book on how to be a first time executor and would be glad to send the link to anyone interested (I purposely did not post a link to keep within the spirit of the talk guidelines). I'd also be glad to answer any questions and share my experiences as a first time executor.