I booked ahead for places in Northumberland and Norfolk over the last couple of weeks.
In both cases I stayed up till midnight to make sure I got the slots I wanted. The week's slots were released at different times for different properties - from12.05 to 12.35. I had my laptop and phone waiting for different properties so I could swoop in as soon as oe was released.
In reality, I think I would have been fine waiting until the morning. There were still some spaces left for the following day for each property when we looked later in the week, but obviously there may not be, the earlier slots tend to have gone, and the booking shuts relatively early for the next day (they print off lists of names and bookings to be checked off on arrival at the property).
I have had success also with English Heritage booking nearer the day. It is obviously easier if you can be flexible with dates and times for any of the sites, which I couldn't be for the Norfolk and Northumberland bookings.
As PP have said, in all the properties I have booked, you got a half hour arrival slot, but once in could stay until closing.
Privately owned properties seem much more flexible in my experience eg I could book much further ahead for Houghton Hall - highly, highly recommended for the Anish Kapoor exhibition in the grounds - and there was no need to prebook for Holkham Hall or East Ruston Vicarage Gardens. Just turn up.
We have thoroughly enjoyed all of them. All well organised, with routes set up or numbers limited when needed, and loads of space for social distancing and picnics. We also always got an outdoor table seat for a coffee and cake, which I don't think we would always have managed pre- covid. I think most people now take picnics. NB. We also took picnics. The flat white or cappuccino was a special treat for each outing after months without. Part of a tentative re-entry into elements of 'normal' life.