If you are only running in a couple of days a week take your kit in on the days when you are in the car or on the train and run with the absolute minimum I have one of those small arm packs that I can fit my phone, work id, a credit card and some money. Cost me about £8 I think. Its much nicer to run without a rucksack and with a bit of planning this can work quite well.
"I live 13 miles away from work so have to rely on public transport."
I also live 13 miles from work but have recently discovered that it is actually 10 minutes quicker to cycle than it is to take public transport and takes the same time if I ditch the underground part of the journey and run to the office from the mainline station.
Perfect way to get fit ,save a fortune and free up time to do other stuff, only works if you have somewhere to shower in the office though as it could be pretty nasty for my co-workers otherwise.