Most recruiters understand that they may not be able to check a reference for someone who has had only one serious job. They will have to restrict themselves to checking character references and checking a reference with your existing employer after you have been offered a job.
If you have made the decision to go to the UK and if you are reasonably employable, why not tell your employer of your plans? As an employer myself, it is really a great help when an employee tells me that they are planning a career change or a move abroad. It allows me to plan for their replacement. It also allows them time off to look for a job and allows prospective employers to contact me for a live reference.
There may be some risks in this strategy in that you will be in a no man's land for some time, but I would think that the benefits outweigh the risks.
Brendan