That's the thing, there is no equivalent of the US copyright office in the UK. The sites that offer the service are private companies, not government agencies.
Canada has a government based copyright registration service.
In the UK, copyright is established (and therfore proveable), by the act of publication. There is no central registration. As far as I know there is no big advantage in the private copyright registration services, though I should check on any court cases that cite a registration. I am not a lawyer. This is all just my opinion and experience.
As I mentioned earlier, the strength of a copyright service is the belief that a jury will have that the copyright claim has not been tampered with and any accesses have been tracked and recorded. Fundamentally, although outwith the UK jurisdiction, a jury would still have a higher level of belief that a song registered with a government agency (albeit a foreign one) would have a higher degree of integrity to a private company.
Additionally you have to think of where the market is and where the biggest threat to your songs would be. That would be the USA. The defacto standard for evidence, and I understand it is essential, is the US copyright service.
All just my thoughts.