Checking in for a flight from MEX-LHR and received this message travelling on a UK passport.

I've searched and found various pearls of wisdom about where and when you can do it at Heathrow but nothing about individual out-stations.

I note my check in confirmation e-mail (haven't tried to print my BP yet) also says this:
"If you are travelling with hand baggage only and have printed your boarding pass, you can go straight to security provided your destination doesn't require a documentation check at the airport."

So, do I have to wait until the check in desks open at Mexico, or is there any way I can do this in the lounge or the gate? If the former, what time do the check in desks open? I've been stranded landside at the airport before due to a mobile boarding pass not working (from Lufthansa) and it's not a great place to be.