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My goodness, Heathrow has cheap hotel rooms a lot of the time, you really would rather crash in a lounge than spend $75 for a hotel room?
(Points are usually a terrible value at Heathrow compared to cash, or I would suggest that but if you had to…)
BA flies from T5 (mostly) and T3 (occasionally).
The PP lounges at LHR aren’t 24 hours, so even if they would let you crash in the lounge you might not be able to stay overnight.
I would be prepared to sleep in the airport overnight if I simply couldn’t bear the cost of a cheap Heathrow hotel room.
https://www.sleepinginairports.net/guides/london-heathrow-airport-guide.htm
sleepinginairports.net
Our London Heathrow Airport Guide contains information about airport lounges, wifi, nearby hotels, hours of operation, facilities and things to do on a layover.