I've done it several times with a large suitcase and heavy carryon. But TWO large suitcases? For many of the tube changes and exits there are stairs (crossing over the platform, going up to street level).

I would say that just getting to a taxi with the 2 big bags will be a pain. Don't forget, you still have the stroll from the tube station to the hostel. Get a ride if you can.

And have fun! I'll be heading over soon myself.