Arrival time at LHR

I always aim for a minimum 90 minutes before the flight, just in case there are delays getting through baggage checks.

The LHR website suggests arriving 3 hours before your flight.

Depends on airline. Which airline is this?
Check on the airline website. Most airlines usually advice to be at check-in 1-2 hours before departure for European flights. That requires to be at the airport a bit earlier.

At least at Terminal 5, LHR doesn't even assign gates till about an hour before the flight. But that also means you may need all the time it takes to get to the gate when it shows up on the big board -- after you've got your boarding pass, checked any bags, and gone through security. I'd give it at least two hours. Or check with the airline.

Sometimes I think the only reason they tell people to get to the airport three hours before a flight so people will have lots of time to kill and they might shop. Or spend money in other ways.

The advice for intra Europe flights is two hours before your flight. Long haul flights are advised as three hours. I would aim for two hours, as has previously been stated T5 is a big terminal and it can be a bit of a slog if you're at one end and your flight is departing from a gate at the other end so if you give yourself enough time to clear security and get your bearings you can relax a bit before working out where you need to be.

Security is quite efficient at Heathrow, I've never waited longer than ten minutes other than when someone in the party has their bag set aside for an additional check.