I'm sure it is a finger fumble, but Heritage Open Days is always September, not November.
The two weekends (two weekends now instead of the previous one) are next weekend (8th and 9th) and the following one (15th and 16th).
Not too many of the London area openings are listed via the link above, that is mostly for the rest of the country. Oxford has a particularly good selection on the first weekend.
Most properties in London which are open are actually open another week later, on the 22nd and 23rd. They will be under Open House London and the link is https://openhouselondon.org.uk/ and there is also an app. Last year the app was better than it has been, but not quite 5 stars, I haven't looked at this year's version yet so I can't say.
Just be aware of queues. The queue for The Treasury, Number 10, The Foreign Office and many others can get quite long.
None, in my experience however, have ever been anywhere near as long as those for The Gherkin, 30 St Mary Axe. I've seen it all the way around the entire extended block and then several hundred yards down the next road.
I've had particularly good times at Lloyds of London , Apothecary Hall, the free walks, and the Foreign Office.
If you can't tell, Heritage days are a high point of every year's calendar.
By the way - you don't have to be in London or England. This goes on all over Europe, usually at the same time as Heritage Open Day (not the same time as London which is almost a week later than everybody else).
I had a really good time one year climbing around in the roof space above St Bavo's in Haarlem. So cool seeing medieval dust.