Hi - I am Dr. Trace and I will attempt to answer your question.
I am not familiar with the health system in the UK and so unfortunately I cannot quote you prices for a procedure called an enucleation in the UK. I am certain you can call and request this information from private practice ophthalmologists.
In the US, I don't know of any surgeons who would remove a viable eye if it still had vision. Removal or enucleation is reserved for blind painful eyes only.
There are many procedures that can be performed on an eye for pain, depending upon the pathology, without enucleating the eye and without decreasing the remaining vision.
Even though you describe the eye as "hardly working", even a small amount of vision will provide depth perception which would be lost if the eye were removed.
I think you need to discuss this issue in more depth with your doctor. Again, enucleation is a last resort for a blind, painful eye only.
I hope this answers your question.