Ah, in London. Right, I don't know where you would start but there are bound to be websites were people are looking to rent for short summer timescales.
Your building society need not necessarily know but this is assuming nothing goes wrong, all they want is you mortgage payments. However if something did go wrong and they did not know this would also invalidate your contents/buildings insurance if you did not have their permission and could cause problems for you.
Best of luck whatever you decide.