Well my take on this is that if yiu are travelling on a british passport you do not need a documentation check on landing at LHR. so if you are HBO and have your Mexico exit slip then try going through. I recall that you go though passport control first.

Otherwise if yiu have amex plat then the Amex lounge at mex is pretty ok. Or the restaurant just down the slope from there (but my imprsssion of that may have been through tequila coloured glasses. )

good of luck and good flight