I have family in the Leicester area and just happened to talk to my mom and dad a minute ago, so they gave me some more tips for you:
If you're going to Southwell - pronounced "Suthel" - you're in the "Robin Hood" area, not far from Nottingham. What's left of Sherwood Forest is in this area. Southwell is also the home of Byron, apparently.
There's no cathedral in Nottingham, but there is a castle. Also near the castle in Nottingham is Ye Olde Trip To Jerusalem, one of the pubs which claims to be the oldest in England (opened in 1189).
https://en.wikipedia.org/wiki/Ye_Olde_Trip_to_Jerusalem
And if you're in that area, they highly recommended Lincoln Cathedral, which they say is one of the best cathedrals in the country. Lincoln is also an ancient Roman city.
https://en.wikipedia.org/wiki/Lincoln_Cathedral
I mentioned Warwick in my previous post but forgot to mention that it has one of the best castles in the UK, although it is a bit pricey to get in these days apparently.
https://en.wikipedia.org/wiki/Warwick_Castle
My parents also recommended Malvern, which is between Gloucester and Worcester. Malvern has a large priory, and is in the vicinity of the Malvern Hills
https://en.wikipedia.org/wiki/Great_Malvern_Priory
https://en.wikipedia.org/wiki/Malvern_Hills
Finally they said that Worcester is a good place to visit. Excellent cathedral, and it was also one of the most important areas during the English Civil War, if you're interested in that sort of thing.