I had the same problem.
I first considered bullionbypost.co.uk as it is running a lot of ads on both tv and the internet. It seems like a big company until I realized that its price were quite high.
I then looked at ukbullion.com. It seems like quite a big and reputable company and its prices are noticeably lower than bullionbypost so I just went for it. So far I bought 1 gold and 1 silver bullions and everything went fine.
Regarding the VAT on silver I don't think there is an easy way to avoid it. You can buy VAT free silver from Guernsey which is an island in the English Channel and then take it to UK, but that would be a bit of a risky operation as it effectively would be smuggling and it would be illegal.