You might want to do a search for "short term holiday lets" or "holiday apartments" in London
My experience is Norwich and not London specific, but we lived in a holiday home here in Norwich for the 1st 2 months after our arrival. I would suggest that route for *anyone* moving here for the first time It gave us time to transition without having to worry about unpacking and getting things sorted right away. Plus, it also gave us an opportunity to properly house hunt instead of having to pick something in a rush.
Our house had everything we needed, bed linens, furniture, cable and internet, cookery items, etc...we just moved in with our suitcases while our things made their way across the ocean. They're a bit pricey, but well worth it in the grand scheme of an international move.