It's a sort of 'yes and no' answer to that one, Hoppy.
There's no obligation upon anyone to register a will anywhere and, as many wills are simply drafted by the testators (rather than using a solicitor) or through a will-writing service, it'll be obvious that many wills are never registered.
However there have been several firms that have tried to create some sort of register, purely for their own profit. That's possibly made matters worse though, as there are several different places where a will might now be registered.
The Law Society has sought to improve the situation though, by recognising just one such service and recommending it to solicitors. It's called the National Will Service and is run by a firm called Advanced. (There's still no obligation upon solicitors to sign up to the service if they don't want to though):
https://www.lawsociety.org.uk/membership/offers/national-will-register