You will struggle to find any offers on NT membership. They don't do discounts anymore, unless it is through an established corporate membership scheme at certain work places.
If you joined the Scottish NT it would be cheaper but you wouldn't actually be supporting the properties in England, N.Ireland and Wales that you would visit. The NTS and NT are two separate charities and do not share fundraising or membership fees. It is a reciprocal membership arrangement and it could change in the future.
If you want to support the properties you are visiting the best thing to do is join the right National Trust membership for that region.