A lot of people are renting in UK now, so they will need permission to install a perm one?

Sure, same here in Germany. Would make the property way more valuable, so a landlord should be thrilled about you wanting to put in that work and could find some arrangement where they need to pay for it only if they kick you out within X years for example

I'd never again move anywhere above ground floor without some form of cooling mechanism, though I've also always been more affected by heat than others seem to. I'll pay basically any premium for this. Currently very blessed with a naturally cool ground floor apartment. The cold in winter I can deal with using clothing, heating blankets, and of course some base heating level, that's all not so difficult nor expensive