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In my opinion, the Konica Big Mini or A4 is a pretty good shout, nice lens, can turn flash off and has a 'close up' mode (which is slightly unnecessary but an additional feature nonetheless).
The Big mini has been steadily increasing in price recently, not quite Mju II prices but edging closer towards an average of £100. In comparison, the konica A4 is still relatively underrated and cheaper than the big mini despite the fact that both cameras are essentially the same, except from branding and name - same lens, body and functions on both but the A4 is less known. Theres currently an A4 on ebay for £50 but I'm not sure how long it'll last for: (https://www.ebay.co.uk/itm/363371659062?hash=item549aa37f36:g:r4sAAOSwZExgg~LX)
Hope this helps. I've got both the Big mini BM 201 and the A4, great konica lens, definitely comparable to the MJU II.
I'm after a 35mm compact of some sort. What's a decent budget option that's small enough to just leave in a frame bag all the time? Would love a Mju II but they seem to go for £100+ which is a bit much for me. I had one years ago that I got for a fiver in a charity shop, I think I gave it away to an ex girlfriend.