SA, if you are not looking forward to commuting, why not try renting a bedsit or a flat in the LHR area during your shift. There are many being advertised in Skyport.
I used to do the 100 mile round trip between Ilford, Essex and LGW, but after dozing off in the Blackwall tunnell twice and getting the wrath of many a white van man after a 12 hour night shift, I decided never again.
I now rent a studio flat in Crawley, it means burning an extra hole in my pocket. But I arrive at work fresh without experiencing road works, motorway morons etc.. however the most important thing is after three or four night shifts in a row, I can get my head on a pillow ten minutes after leaving work, and believe me this at times is HEAVEN.
Congrats and good luck with your new job.