I agree. Very cheeky indeed!!
I was on a graduate trainee scheme too a few years ago based in Leeds and after 1 month they asked me to move to London to work on a company merger. The company paid for my accomodation and evening meals for 7 months (although it was a just a scruffy room in a house in Ealing), but they didn’t pay for my travel expenses from Leeds. I thought that was bad enough at the time TBH, as I hated living down there and travelled home nearly every weekend, but at least they went some way towards being covering my expenses.
My advice is to check your contract of employment first. Does it define the location of your regular place of work? If it does & they are asking you to work somewhere else, then they have an obligation to covering your expenses. I doubt you’d be able to claim back expenses from the tax man, but check it with a qualified accountant to make sure you make the most of what might be a crappy situation. If they don’t change their offer, I’d be asking myself if I really want to stay with a company that treats me like thatin the longer term though!!