Sorry, but it's impossible: Starwood has zero presence in the touristy parts of England beyond London.

The best you could do would be to have four or five nights in London and three nights at the Sheraton Grand in Edinburgh (which is in a different country, Scotland).

But you also need to ensure that you also visit the other major tourist attractions in England, which is impossible through Starwood.

The places I would be going to are:

1) The Cotswolds,
2) Bath (ancient Roman city)
3) The Lake District - consider a hotel like Sharrow Bay - google it.
4) Chester as a day trip from the Lake District if you didn't go to Bath.

If you just go to London and Edinburgh you will waste your trip.