There may, of course, be signs up at Greenwich Park (of dubious leaglity since their Bylaws make no mention). But if not … if it were me … I’d find a quiet area and go for it.
You have the benefit of not being British … so arguing forgiveness should be OK.
One additional thing - still new for the UK - is “DRES” (Drone and Model Aircraft Registration and Education Scheme (DRES) ).
It’s a very small fee that needs to be paid after passing a very simple online test - (details in that link) … after which you get an ID number that you need to find some way to print and stick to the drone (if over 250g).
Now - just for a couple of days? I think I’d repeat the “asking forgiveness” bit. I’ve travelled and flown without being fully certain of the local dos and don’ts for a particular location (I could at least blame that on my poor Italian/German/French. 
) … but take a look and I’ll leave that decision to you.