First of all, Quantum computing is not really an area, it is more a "theme" which includes related work in many different fields:quantum optics, NMR, ion traps, superconductivity, computer science etc.
Hence, working on "quantum computing" can mean anything from coming up with new algorithms (computer science/math) to fabricating structures in a cleanroom.
Secondly, unfortunately you picked the wrong country. There is almost no serious work on QC in the UK. There are a few groups (e.g. an algorithms group in Cambridge) that work on QC and related areas but most of it is just "spin off" work resulting from other activities (i.e. "we have a new device and one possible application might be in QC").
The reason for this is that it was decided a few years ago that UK should NOT pursue QC but focus on other quantum technologies such as quantum cryptography (where there is quite a lot of work going on) instead. Hence, it has been virtually impossible to get any QC related work funded over the past few years.
If you really want to work on quantum computing you should go to the US (where I would guess 90% of the work is done), other countries to consider are Canada, Australia and Japan.