Are there any?
Salisbury seems to be the mostly likely, according to previous posts, but your guide will have this information at the beginning of the tour.
I'm in the group starting May 23.
I am on the South England tour right now (final few days) and I did laundry in Salisbury at the Washing Well. Just know that you need exact change of one 50 pence and one 20 pence piece exactly to obtain the laundry detergent. Also make sure you have pound coins to operate the machines. It’s very expensive. For one regular-sized load, it cost 8 pounds (5 to wash, 3 to dry). I did it on a Saturday, which meant I couldn’t just drop it off and have the laundromat do it for me. Monday-Friday you will have this option, which is far more convenient than waiting around for your loads to finish.
We took this tour 3 years and there was a laundry opportunity. Do not remember which town.