ATCNoob.. Methinks you should have thought this out much sooner!! Chances are that you will have to move before long. There are other places you could be posted apart from Swanwick and even at Swanwick you would find it very difficult to get there for some of the shifts by public transport. Some of the TC shifts start at 6am, not 6.45.
I wish you luck but urge you very strongly to get driving. It's unthinkable that a working family man should not be able to drive nowadays as public transport is hopelessly unreliable.