In fact, on Wyeast's website, their description says,
"London Ale III is Wyeast's strain cultivated from the Boddington's brewery, long famous for their creamy pub ale. "
No it doesn't - the lawyers of the yeast labs make sure that they are almost never seen to be using a brewery name to sell yeast, it's all done by nudges and winks. The Wyeast page for 1318 actually says :
https://wyeastlab.com/yeast-strain/london-ale-iii"Originating from a traditional London brewery, this yeast has a wonderful malt and hop profile. It is a true top cropping strain with a fruity, very light and softly balanced palate. This strain will finish slightly sweet. "
You have to take all the traditional attributions with a slight pinch of salt - many of the Wyeast and White Lab strains have their origins in homebrewers harvesting them, and there's plenty of scope for mixups and mislabellings, plus strains mutating away from the original - for instance WLP002 and 1968 are confidently said to be from Fuller's, but lack the marmalade-ness that is so characteristic of the actual Fuller's yeast.
The whole Boddies thing is a mess as well - they lost their original yeast when the brewery was bombed in WWII, they restarted production with a yeast from Yorkshire that gave crazy-high attenuations (
over 90% in the heyday of the 1970s), then there are dark rumours that they lost their yeast at the start of the 80s, then when production of the cask was contracted to Hyde's the Boddies yeast never took to Hyde's kit and they ended up using the Hyde's yeast instead.
And of course they were bought in 1987 by Whitbread who had possibly the biggest yeastbank in the country.
There's been suggestions that 1318 has some kind of connection with Courage, either directly or indirectly, which at least would put it in the right city!
Going back to the OP, the traditional Burton yeasts traditionally had very high attenuation (which meant that there wasn't much sugar left for secondary fementation, which you don't want for export beers travelling a long way through the tropics). If you're wanting to be a purist about it then Brewlab are your best option - I don't know what the current status of their deal with Hop & Grape is, but they're still listing slopes for sale like their
Burton.
WLP026 is a rare Vault strain that's probably the closest pitchable yeast, WLP023 would probably do. Or just use something like Notty (or even a saison strain, fermented cool), it's more in keeping with the cheap and cheerful ethos of mild....