Happy Monday deal has just started again, and London Ibis Heathrow and Ibis Gatwick are available on 31/12 for £25, plus currently special offer of 7.5% TCB. Family room has new Ibis SweetBed (double) plus a full single bed (not a sofa bed/camp bed like some chains).
Combine with TfL offer of free travel for all. This hotel is a Piccadilly line tube ride from central London, frequent takes about an hour but loads of stops throughout London so is convenient.
Then a 5-8min bus ride from Heathrow Airport Central Bus Station, 24 hours, every few mins every night, these are totally free all year round anyway as are in Heathrow free travel zone.