We have a 2 week self driving trip planned from London, Bath, Cotswolds, Stratford upon Avon, Pilsley (Peak District), York, Durham, Bamburgh, and Edinburgh. We have HHA memberships and plan to visit Highclere Castle, Chatsworth House, Castle Howard, Alnwick Castle and Bamburgh Castle along the way. I would love to hear about your favorite HHA along this route so that we might visit them, too. Here's the HHA link http://www.hha.org.uk/
Harewood House was fantastic. It's filled with original Thomas Chippendale furniture, interior details by Robert Adam, and beautiful gardens. It's not part of the HHA scheme, but worth a visit. BTW, Alnwick Castle is a must see.
I don't think it's part of HHA but Hatfield House is one of my personal favorites. It's near St. Albans just north of London. The family still lives there and it was where Elizabeth the 1st was staying when she learned she was queen. The house is filled with history and the gardens are beautiful!
Agree with Anita re Hatfield House. You can't take photos inside but the guided tour is very nice. Gardens are gorgeous.
Chatsworth is huge! Awesome gardens which seem to go on forever.
Highclere is definitely a must for Downton Abbey fans.
Spencer House in London is worth a visit, but it is only open on Sundays.