Discount Card for Castles and Palaces in England?

Historic houses in England have a mix of different owners. Some are owned privately or by a trust, others are run by an organisation.

So as far as I know, there’s no one card that covers all of them.

Look at these organisations:

National Trust
English Heritage
Historic Royal Palaces
Historic Houses

If the sites you want to visit all belong to the same organisation, then it’s worth joining. For example Historic Royal Palaces covers both the Tower of London & Hampton Court and can be worthwhile.

However from memory, both Blenheim Palace and Chatsworth House are independently run and owned, so I don’t think there’s going to be one card or membership that will cover everything.

What about the 2 for 1 card that can be purchased at a train station?

2 for 1 card rarely if ever includes admission to the locales listed by the OP.

We use Historic Royal Palaces, which includes Hampton Court Palace, Kew Palace, Banqueting House (small, often over looked place. Beautiful and worth a visit. Great history), Kennsington Palace, Tower of London and Hillsborough Castle (N. Ireland). Great deal and comes with a nice book. Doesnt include some of the places you're looking at, but might be worth adding some of these to your itinerary if possible.

Treasure Houses of England which includes Beaulieu, Blenheim, Burghley, Castle Howard, Chatsworth, Harwood, Hatfield, Holkham Hall, Leeds Castle and Woburn Abby has 2 for 1 Vouchers (advance purchase} available for pickup at each venue with some conditions. Look their official site for more info. They used to have a pass for all of these but I don't believe that it is available anymore...but you could inquire.

Thank you fellow travelers for all the helpful information!