When I think of progressive towns/cities in the US, I think along the lines of Portland, Oregon; Chapel Hill/Carrboro, North Carolina; Burlington, Vermont, etc. I haven't yet come across an equivalent in the UK, to be honest. I suppose some people might say Cambridge since it's a big university town but I don't really think it compares.
What one considers progressive can really vary, but having lived in both Chapel Hill and Carrboro at different points in my life, for me, one of the biggest factors included political involvement, especially at the local level, and a big focus on social justice issues as it pertained to the town itself. Another would be the huge importance placed on town infrastructure and how it affected the daily lives of residents--for example, not only was the public bus system pretty far-reaching and developed, it was free for all residents to ride, and you could store bikes on a rack at the front of each bus, which eliminated the need for taking a car to school/work. Both Chapel Hill and Carrboro grant domestic partnership benefits to same-sex couples even though the state of North Carolina does not, which also speaks volumes about the kind of towns they are. Other factors for me would be an emphasis on local produce and goods, a lack of chain stores and restaurants, a thriving arts scene, strong presence of farmers markets and cooperative stores, and an emphasis on community events and education.
I've seen certain elements of these things across the UK but haven't yet come across a town that has an overwhelming sense of all of those things combined.