Would a late night coffee shop/tea house work in the UK?

There is some demand... but it can be complicated and the costs are higher than in many other countries. Staffing costs, lease costs, plus you can wind up needing an 'events licence' if it's open late even if it's not putting on events. You will be having to deal with drunk rowdy people who have been kicked out of pubs, who are under the impression that having a coffee will sober them up a bit, so you may well need security on the door anyway- the council may insist. You can basically wind up with almost all the costs and complications of running a bar, but without the income from selling alcohol. If you do start selling alcohol, well, you just opened yourself up to UK drinking culture. Maintaining a quiet and chill vibe would likely mean turning away customers. Heavy drinkers spend a lot more than someone having 2 coffees and a slice of cake in an evening. There probably are places it could work, but it's not likely to be easy.