None of the homebrew yeasts are like the real Fuller’s production yeast - the real thing has an orange-marmalade character that you just don’t get in typical homebrew yeasts - except apparently Imperial A09 Pub and maybe the Omega one (OYL-016 ?) But WLP002 and 1968 are not the same as Fuller’s yeast. Maybe they did originate there and they’ve mutated into something blander, maybe they never saw Chiswick in their life, I don’t know. You do need a yeast with character for British styles, and 002/1968 are a bit boring.
If you want Fuller’s yeast, get it from the source - harvest it from cask or one of their bottle-conditioned beers like 1845 and IPA/Bengal Lancer. And if you want the actual Fuller’s recipes direct from the source, see this thread on HBT, there’s a homebrew version of ESB in post 42. Note that although I’d say the Fuller’s partigyle is definitely at the high-crystal end of the British spectrum, they’re only using 7.2% light crystal - nothing like the heavy-handed use of crystal you see in some US recipes for bitter.
EDME should be capitalised, it stands for the English Diastatic Malt Extract Company. They were a major supplier of homebrew kits in the 1970s/80s, but got out of that business in the ?1990s?. So their yeast was popular just because it was easy to get hold of and it appears to be the ancestor of the Munton/S-33/Windsor family, I’d guess the master cultures would probably have ended up at Munton if anybody. One has to assume that Mangrove Jack M15 is a repacked version of one of them. I only know Windsor - it’s a classic example of a yeast that drops well but doesn’t flocculate, so you can have a clear beer with a yeast cake that puffs up at the slightest disturbance. But it’s pretty common here to add a bit of Nottingham or S-04 after 48 hours to help stick it down.
Lallemand London/ESB is apparently from the same multistrain as Windsor and seems to be a blander version of Windsor and a bit pointless in my eyes - a bit like Munich versus Munich Classic only without the option to rebrand it as a wit yeast.
They’re close to T-58 and BRY-97 as well - what’s your point? Yeast doesn’t know what it’s meant to be for, historically the same yeast would have been used for beer, bread and distilling - in fact beer is a useful way to grow up yeast for use in bread. (I actually have a starter of bread yeast going at the moment, since the hoarders have bought all the yeast in the shops). The fact that one particular strain has become so dominant in US bread is a quirk of history that says more about the commercial structure of the bread industry than its qualities as a bread yeast. I’ve not had the chance to compare the two but it sounds like the typical US bread yeast is different to the main UK supermarket bread yeast, which actually behaves quite well in beer IME.
I made an ESB with Nottingham a couple of years ago with wet hops (willamette) and it was pretty good. I then dropped a barley wine on the yeast cake and I thought that was good too.
On the Maker’s Mark Distillery tour, I recall hearing that Bill Samuels would bake bread to determine the ingredients to use for his elixir. I believe that included yeast.
I’ll be honest, I’ve tried the Lallemand London ESB strain a few times, and I didn’t find it to have the flavor I was looking for. The best I’ve gotten from dry yeast is Windsor (co-pitched with Nottingham to improve attenuation), but even that’s still not as flavorful as my preferred liquid yeasts. I plan on trying the new Lallemand New England in a bitter, since I’m assuming that has English roots, but as of right now if I really want a bitter that checks all the boxes for me it’s gotta be WLP002 or WY1469.
I had forgotten about old reliable WLP002. I recently pitched one pure pitch pack directly into 1.036 wort for a bitter and it was done in 4 days at 62F. I racked it at 7 days and it had sedimented yeast well packed down and was pretty clear (for a Brit Ordinary Bitter). Started drinking it after 3 days on the carb at 10 psi - wonderful. A good running ale to have on hand (as long as it lasts).