You should be wary of anyone offering Burford Brown (or Cotswold Legbar) eggs or birds. These names are the trademarked property of Clarence Court.
The only known legitimate breeders of Burford Browns are Legbars of Broadway. They created the breeds and retain the right to use the names, having sold the rights to Clarence Court, who supply table eggs to major outlets.
Legbars of Broadway don't sell hatching eggs or male birds. So the only way you can have real Burfords would be to buy hens from them. Of course, you can then use some other breed of cockerel to cover those hens, but the offspring will be "mongrels", not true Burfords, and should not be sold as such.
I dare say that rigorous selection of the best of their offspring, and the weeding out of birds showing too much of the cockerel's type, would eventually lead back to something very similar to a Burford - but you still could not legally call it a Burford Brown.
The breed is generally believed to be substantially derived from French Marans (although it's exact makeup is a trade secret) so these, and perhaps the similar-looking Blackrock have sometimes been added by inscrupulous breeders. But of course, that doesn't make the progeny Burford Browns.
I have bought hatching eggs on eBay from Mirrorbrook, and I am deeply disatisfied with the results. The birds are now fully 8 months old, but very small, even allowing for their relative youth. They vary considerably in build, plumage and comb. But it is their eggs that are most disappointing. Only one bird lays an egg that might pass as a Burford Brown egg - which should be very large, deep brown, smooth and glossy. The rest of the hens are producing quite small, paler and matt eggs. One produces an egg that reminds me very much of a small French or Cuckoo Maran egg.
I have complained, but Mirrorbrook refuse to accept that the breed name/type is trademarked and, at the time of writing have declined to deal with my complaints about the poor quality and inconsistency of the birds.
I recommend you approach Legbars of Broadway for your hens. They have approved stockists, including one at Malvern, Newlands Poultry, who can supply you with true Burford Browns.