If he has all the correct paperwork then there is no problem bringing a dog into the UK. As long as he has been treated for ticks and worms between 24 and 48 hours before entering the UK and has had his passport validated by a vet who is qualified to do so, then there's no problem. Not all airports or ports are licensed to accept pets into this country though.
I would, however, check that all the paperwork is correct as you in the UK only dogs over 6 months old can have the rabies vaccine and it takes another 6 months - minimum - to complete the procedure. So in the UK, your dog would have to be at least a year old before it's pasport is valid. Some EU countries accept dogs 21 days after the vaccine has been given but Britain requires that the dog is blood tested 1 month after it has had it's rabies vaccination to check that the vaccine has worked. The animal can't re-enter the UK until 6 months after it's had a satisfactory blood test.
Have a look at www.defra.gov.uk for full details as if the paperwork isn't complete your dog will have to spend 6 months in quarantine.
(I had to edit this as I got the procedure mixed up a bit but I think it's right now)