I'm not specifically recommending them as I haven't been (and I often find museum exhibitions lacklustre) but these are on my list to check out next time I'm in the UK in the appropriate areas:

Manchester is where the important early computer development in the UK occurred; Turing spent a lot of time working with the Manchester Baby: https://www.scienceandindustrymuseum.org.uk/whats-on/meet-ba...

Reading was Digital Equipment Corporation (DEC)'s centre in the UK. While it was an American company they had a huge estate here. I have a soft spot for their machines so I'm curious to see what this small museum managed to pull together - I know they reached out in some of the relevant Facebook groups for personal stories of DEC and their machines: https://www.readingmuseum.org.uk/whats-on/reading%E2%80%99s-...