Hello there! Most members here are in the USA, but there are plenty of us from the UK here as well as many other countries around the world!
Silver tabby isn't a breed, but a colour that is found in many many different breeds of cat including moggies. If you like the British Blue, the breed is now called British Shorthair and is available in most (if not all!) cat colours, not just blue any more. Silver tabby British Shorthair kittens are a popular choice so if that is exactly what you want in a cat, then I don't think you'll have too much trouble finding one.
Do your homework before choosing a breeder, as unfortunately there are a lot of unscrupulous people who breed cats just to make money and don't care for them properly. When I was looking for a pedigree kitten I went to a few cat shows to see what the different breeds and colours look like in person and to discuss with breeders the personality types of the different breeds to decide which was best for our lifestyle. Then we arranged to visit breeders to meet their cats and kittens. Kittens should be raised in the home so that they want human contact and are used to household noises. If a breeders home is smelly or dirty or cats are kept in cages (queens may be caged just before giving birth and when the kittens are tiny, this is for the safety of the kittens before they can see, hear, and walk, and stud cats will have separate housing which may be outdoors but should be clean and roomy with things to climb and play with and heating in an indoors part for cooler weather, this is OK but longterm caging of all cats is not good) or cats look sick or are frightened of you then do not get a kitten from that breeder. A good breeder will ask a lot of questions about you and your family, and want to meet all of you to see how you interact with the cats - they are not being nosy for the sake of it, they want to make sure you will provide a good home for one of their babies, and to help match the right kitten to the right person - if they do not seem bothered where their babies will end up or what kind of life they will have with you, then avoid! Meeting a breeder should be a 2 way interview to make sure that you will get an excellent companion and that their precious little bundles are going to be cared for and happy. Many breeders prefer their kittens to go to indoor only homes because of the risks of traffic, theft (unfortunately theft of pedigree cats is rife), parasites, and disease.
A good place to start looking is a google UK search of British Shorthair clubs and societies (there may be some that specialise in tabbies which will help you to narrow down your search), they will be able to help out recommending a breeder who has kittens available or due soon. Breeders should be registered with one or more of either the GCCF, TICA, or FiFE (Felis Britannica), the 3 main registries for pedigree cats in the UK.
Good luck with your search! And if you decide that a pedigree cat is not for you and you would just like a cute little silver tabby of any or no particular breed, then the cats protection league, RSPCA, and local cat charity shelters and rescues are excellent places to look for your ideal companion.
EDIT: As far as jabs go, if you get a pedigree kitten then it will already have been vaccinated and microchipped and the breeder will give you the vaccination record which you should take along to your own vet, a new kitten should still have a vet visit to register them at your vet and check they are healthy within the first couple of days of you bringing them home. There will be a microchip owner transfer form to send off too, and registration transfer papers (if registered with GCCF this is known as 'the pink slip' because it's... well it's a pink slip
). Don't get a kitten too young - breeders are not allowed to home kittens until they are 13 weeks old as this is how long they need to spend with their mum, you will see many adverts for moggies as young as 8 or even 6 weeks old but this is TOO YOUNG to leave their mum and behavioural problems are common, they should be 10 weeks at the very very least. The only exception to this is of course if orphaned kittens are in a shelter, they gain nothing from staying longer once they are weaned as they have no mum to learn litterbox habits and proper behaviour from, although they do require a lot of patience and may need help with toilet training, not scratching and biting hands and feet etc.
Spaying/Neutering should be done as young as possible, but most UK vets won't do it until 5-6 months old so be guided by your vets advice on that one
Be aware though that female cats can get pregnant as young as 4 months old which is very bad for their health, and male cats can get a female pregnant from around the same age, so if they are going to be allowed outdoors this should wait until after they are spayed or neutered (once the stitches are out for the female but wait a few weeks at least with males as they can still get a female pregnant 1 to 2 months after neutering) to prevent any accidental kittens and to prevent roaming long distances in search of mates.
Sorry that response was so long, I do hope it was useful though!