I've often said there are two types of people; personally I don't think I'd go in to town - landside a 20 min walk or a short cab ride maybe, but chugging in to central London would add unnecessary stress on the way back if anything went wrong so I'd rather stick close enough that a broken down train couldn't leave me missing my flight or needing to commando-roll through the gate. Some people seem quite happy aiming to rock up to check in 45 mins before departure though, so if that's you then it's doable, just doesn't sound very relaxing to me.

My concern would be more about public transport/central london traffic than airport security though.