How long is a piece of string ?
It's very much going to depend on how big the house is and how much clutter / hoarding there is on the side of clearing the house, and how much the executor knows about the estate and whether there is IHT to pay in terms of probate timescales. Also how local you are - we live hundreds of miles away so have had to do it in bursts of weeks at a time as we can.
From my current experience - mum died in mid-june and I spent the week or so after her death in the house notifying all the relevant companies and arranging the funeral, We then came back for around three weeks around the funeral in mid-July doing an initial sort of the house contents. They weren't great hoarders so it wasn't too onerous a task apart from the paperwork - dad (who had died a couple of years earlier) dealt with everything by post / hardcopy and kept everything going back decades in the form of bills, invoices, letters, payslips etc.
We went through all the rooms and found all the sentimental / personal items I wanted to keep and got them out the house. As I'm the only surviving family member and sole beneficiary I don't need to consult with anyone else which greatly speeds things up. I also got three estate agents round to value the house.
I then spent time filling in the IHT forms (there is no IHT to pay but I needed to claim the additional residential IHT allowance) , and could send those off to HMRC by the beginning of September. Although they say allow up to 12 weeks, I got a response from them in early October giving the go-ahead to apply for probate, which I did straight away and although that also suggests a timescale of up to twelve weeks that came through just over a week later.
So just over four months between death and getting probate. You don't need to have probate to get the house on the market, just to exchange contracts. We're now down for another week decluttering the house ready for it to go on the market. We're leaving most of the furniture but putting a lot of the ornaments etc in the garage and will get house clearance in once we have a sale.
Hope this gives some idea - but as I say it;s going to be a very individual experience depending on circumstances, amount of clutter, family dynamics etc. .