You can usually get the LHR Renaissance for about 55-65GPB including VAT w/ AAA or weekend rate. It's a haul on Picadilly line back/forth to Central London, but can be done. I've stayed there a few times when I needed a cheap rate & also wanted Marriott points. Also, it's easy to get to LHR using the free red busses that stop outside of the hotel. Central London cheap places I'll defer to the London folk.

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Sharon