Short answer is that nobody knows how many are carried out in the UK. because we have precious little data to go on. Hospitals have not been obliged to document and report instances of FGM, although the practice has been illegal since 1980s so quite why it was not mandatory to document and record such cases before now I don't know.
The only figures we do have are based upon the returns from a small number of hospitals, mostly situated in London, and it is from these figures that the overall figures for the incidence to be extrapolated and guessed at.
I thought it interesting that, of the 4,000 or so cases recorded, only 8 were actually born in the UK; This seems to be very much a problem with new immigrant communities, although that perception might change as more figures come in ,and suggests that those offering to perform FGM are situated abroad for the most part, rather than being based in the UK.
As to medical professionals over here "getting their fingers out" and reporting more cases - they can only report the cases they see, and most often they present later, during pregnancy etc. I do not suppose GPs for instance, make a habit of inspecting the genitalia of young girls unless there is a pressing clinical need to do so; nor should we want them to.
As with all things, education remains the key factor in changing the cultural perception of FGM and rendering it obsolete ; Education within the communities and education of those girls at risk.