What time is it? Watches and horology

Take a look at the new 39mm King Seikos. Nice finishing on them (not GS level, though) and quite a nice bracelet. They're not the slimmest watches ever but not overly thick. There's a blue dial option:

https://www.seikoboutique.co.uk/product/king-seiko-tamahagane-ksk-spb371j1/

I prefer the smaller 37mm version personally but I don't think there's a blue dial option for those, and they don't have a date.

Or the 40mm blue dial SBGP013 quartz Grand Seiko from a reputable retailer like Watches of Mayfair, which is a smidge over £2k new:

https://watchesofmayfair.com/brand/grand-seiko/all-grand-seiko-watches/grand-seiko-heritage-quartz-40-mm-sbgp013

With a second hand Grand Seiko you have to look really carefully and make sure you're ok with the condition because the polishing on the case is so high, they really up show any scratches. One of the nice things with a lot of the quartz models is they're brushed on the bracelet and the top of the case so they're not quite so shiny as, say, a 44GS case is.

At the lower end of your budget there's a blue dial variant of the "Style 60s" Presage which is around 40mm: https://www.seikowatches.com/uk-en/products/presage/srpg05j1

Or, even cheaper, there's a blue dial version of the 40mm Seiko 5, SRPE53: https://www.firstclasswatches.co.uk/seiko-5-sport-automatic-watch-blue-dial-stainless-steel-bracelet-srpe53k1-p-59393/

I have kind of assumed that blue is part of the brief but there are other colour variants of all of these watches.