Just a thought - YMCA'S ?
Years ago my Dads firm relocated and being in the middle of my A-levels the disruption would have messed things up so his firm sponsored me to stay in the local one for my final year. It had a corridor put aside for females.
They have probably changed a lot but it might just be worth checking out if there are any in the towns near to Heathrow. It might work out cheaper than a guest house and more sociable in the short term.
When I was there about 80% of the people were young professionals who had moved to the area to take up jobs, They usually grouped off and rented houses to share.
I had a lot of fun and don't recall God having anything to do with the place. It might be worth looking into if you really get stuck.
Best wishes,
TB.