Note that the 'UK Copyright Service' is a private business and not an arm of government or the judiciary, however official looking their stationery is.
The UK doesn't have a 'copyright register' (the US is pretty much the only country which does, and since they signed up to the Berne convention it is now more of an optional extra than a requirement even there.)
What the 'UK Copyright Service' appear to be doing is basically saying register with us, and then if you end up in a copyright dispute we'll turn up in court to say "yeah, he sent us a claim to copyright in the work in 2008." How much attention the court pays to this is up to the court.
In a copyright dispute, you need to be able to convince the court that you are the original author of the work. If you shoot film, this is fairly trivial - you have the negatives and the infringer doesn't, so game-set-and-match. For digital works this can be more difficult, and that's where 3rd party intermediaries come into things.
The old fashioned cheap way of giving yourself some evidence of copyright when I was a lad was this: Place copy of copyrighted works inside an envelope. Sign across the edge of all seals on the envelope, and then cover with sticky tape (i.e. it should be impossible to open the envelope without evidence of it having been opened being obvious.) Post envelope to yourself registered post. Stick envelope once you've received it somewhere safe.
If you need to roll up in court to prove you authored the work, you can use the Post Office stamp on the envelope with the date as evidence that you possessed the work before any of the alleged infringing works were produced.