Yeah basically much like Gotham they've taken bits and pieces from all the various Multiverses and used it in this show.
The Michael Caine Alfred was pretty much ex SAS (it's how he played it anyway) and given the accent used in this show that's where that Alfred is coming from, as they did a retcon in the comics based on that in 2014: https://www.bleedingcool.com/2014/11/05/alfred-pennyworth-now-officially-of-the-s-a-s/
That also mentions other versions of Alfred, the Royal Marines part was one were Alfred met Thomas Wayne during a tour of duty in the Middle East and the two became good friends. Alfred has also been a classical trained actor, been in MI6, and a combo of both those at one time with his acting being his cover.
They've taken some of the comic Batman: Holy Terror as well and kind of used some of that timeline and used the Thomas story for Martha and Alfred, as in:
"It depicted an alternate timeline where Oliver Cromwell established a theocratic government across the globe, Thomas Wayne is the chief physician of the Privy Council, but when it is discovered that he is treating various 'enemies of the state' such as Jews or Homosexuals, the Star Chamber votes by secret ballot to have him and Martha executed and make it look like a random mugging."
Which is a bit of play on Martha and Alfred saving those gay guys, which of course was also a play on English mathematician Alan Turing and his story during and after World War II, plus the look has a touch of the animation Gotham By Gaslight.
So yeah basically it's using the lesser known stories out there and mixing it in a big cauldron much like Gotham did to create another timeline, which makes it very interesting for mine as both Thomas and Alfred have been though various backstories (Thomas was even Batman once).