You do end up paying roughly twice as much for accommodation to be in London... my friends elsewhere pay £70 a week to live in a house with 2 bathrooms, a living room and outdoor space. I pay circa £140 a week in a piddly flat where the 'living room' has become a third bedroom to cut costs. So yes you will probably live in an expensive box. By commute do you mean just getting to placements? Most are within London, but I imagine you have to travel a lot at all medical schools public transport wise.
Whether it's 'worth it' isn't something anybody can quantifiably tell you. It may be 'worth' it to one person but not to another. I'm not sure worth is the best way to go about it.