You can check with the Dominican Embassy in the UK, but I know of no way to renew a cedula without coming back to the DR. My wife was born here in the DR and she said that in the past, if your cedula expired, you could just get a new cedula the next time you come back to the DR and you return to the same office that gave you your cedula before. Again, best to verify this with the embassy. This "return to the same office" requirement may have changed. I am sure many people face this issue.
It is best to double check exactly where you need to renew. For example, when she renewed her passport, we had to go to Santo Domingo. Before, she had to renew her passport in the closest office to where she was born.
Out of curiousity, of what value is a Cedula in the UK, or do you just not want to be current the next time you re-enter the DR?