If the flat/house is already "plumbed-in" for Sky you could pick up a second hand Sky box for under £25 plug it in, link it to the Sky feed and get the benefit of all the free channels broadcast by Sky.

As for the digital signal for your Freeview TV - if you can install an aerial that is higher than the trains and thereby the trains do not block the virtual line-of-sight with the transmitter - that may solve your problem too.