Ok, you only need to be able to get to LHR within 2 hours whilst on home standby during a reserve month. On SH, typically 1 reserve per year, LH 1 per 18 months. During the reserve month youi'll get lots of trips and not a huge number of standbys...bit of a bone of contention in that you get hardly any standbys at the moment due barely enough pilots to cover the work.
In your case, like hundreds of others just spend the 6 hours in a service station (has been done) or stay at LHR for most of the 21 days you'll be on reserve (you can get home during the long and short breaks you'll get). I'm afraid sitting around Compass can be boring but if Ops know you're in the building they know you can fly at short notice.
To put it in perspective, you'll be affected by the 2 hour rule for approx. 6 days per year (2 standbys per week (just my experience and not fixed) per week of reserve). Everyone puts their life on hold for 18 days on reserve (21 minus min of 3 days off in that time)
If you can handle the commute on normal duty days you can come up with a solution for the few days per year you're on standby.