You will be expected to travel to anywhere your clients are!
And this isn't meant to be a facetious reply - you will have to work where your clients are based. If you are going in at Consultant grade, you will have little to no say in terms of your client base. As you build relationships and progress, this will start to improve.. but to be honest, very slowly and not massively.
In my few years at a Big 4, I worked all over the UK. Some of my peers worked all over the world. It really just does depend on your clients (and therefore to some degree your industry focus - e.g. FSI is more likely to be in London).
What you have to realise is that you can't be seen to be using location as a driver for your selection of projects, as that doesn't make you look like the flexible and adaptable consultant that progresses quickly up a Big 4 firm. Truth be told, you probably wouldn't anyway... if you had to choose between a project in the depths of nowhere but with excellent development prospects, against a PMO turn-the-handle role in the middle of London, you will probably choose the former. If you're not 'that' type of person, you'll probably have a short lived career in consulting anyway... so I wouldn't worry too much about what is likely to be a short term problem.