Due to LHR curfew there are no 24 hour lounges.
Some of the public buses to nearby suburbs, which stop along Bath Road (free) where the airport hotels are, run 24 hours. The buses leave from central bus station. Some of the airport hotels are only GBP19 + tax.
The hoppa bus (GBP4) isn't 24 hours but runs until fairly late and resumes around 0430 IIRC.