Hi Brad -
Good idea to drop the Travelodge idea; they are and Premier Inns are the best cheap UK hotels but in my experience they require your keycard to even get out of the reception area so that you can get to the corridors and lifts (some even need the keycard to open to the main front door I think, late at night.) You'd have to accompany anyone in basically, which is do-able, I've never been questioned by staff about that, but only taking in one guest. More than that and I've heard they sometimes surprise people with an extra charge for a "cot" in the morning! The receptions and lobby areas are very small. Also the Vauxhall one is noisy the higher up you are because of trains.
Vauxhall and Lambeth are great areas for gay venues and gay residents but the horniest guys will be willing to travel that little bit across the river. Holiday Inns seem the best chain hotels for discreet access to rooms here (I live in London), and I've heard that the Russell Square / Bloomsbury one and the Kings Cross one are easiest (and I should *ahem* be able to confirm that personally sometime next week, haha!) I think there may be a difference with the the Holiday Inn *Expresses* (as opposed to Holiday Inns) There's one of those at Vauxhall too a stone's throw from the Hoist. Have you been to the Hoist before? Or the Vault? Afraid I don't know much about the Mayfair or Gloucester Road HI's, but they will put you near the V&A, History Museum, Science Museum, Knightsbridge.