I did it. If property is part of the estate, and if the inheritance is from a parent, who inherited everything from their spouse, IHT isn't payable for estates under a £1 million.
I sent my parent's death certificate to relevant banks asking for a final account of any money they held, I valued the estate by asking two local estate agents to write me a valuation and used these figures to value the estate - you need that figure for the probate application.
I applied for probate via the online form at gov.uk and sent it in. I had to pay a fee online to get plenty of certified copies of the probate grant. Probate was granted about 10 days later and I sent the probate forms to any banks who hadn't yet closed my parent's accounts and they paid the money to me (some had already done that on receipt of the death certificate).
Important points: I was the sole executor and sole beneficiary of my parent's will. They had inherited from a mirror will from my other parent, and no IHT was due. If the will had been more complicated, I might not have done it myself, but it was very simple and quick for me to do in my circumstances.
I signed up to the Which? free legal service for the duration, I think it was £9 a month, you get unlimited phone advice from their expert advisors, and I only needed two phone calls to sort it out. Take a look at gov.uk, there's lots of guidance on the forms.