You couldn’t make Little Britain today mostly because it wasn’t very good, and the standards of the time were lower.
You could absolutely remake The Day Today, Brass Eye, Goodness Gracious Me or Peep Show today and they’d be just as good.
I really distasted it when it was running.
At the moment post 1997 when Britain was starting to change and become more diverse and sure of it itself it reinforced an identify of Britain as it used to think of itself: silly voices, binary identities and oddballs.
It has more in common with Love Thy Neighbour than anything that came after.
https://m.youtube.com/watch?v=jF-CkMpQtlY&pp=ygUUdmlsbGFnZSB...
This business where we're all supposed to be surprised by what Russell Brand was up to despite him being incredibly open about it at the time is the same thing: society wants to blame the highly visible individuals of that era but in truth it was the audience that wanted this stuff that were the problem.
I still hold that special up as one of the best pieces of satire to ever air on TV, but at the same time I'm shocked it was ever able to be produced and shown since it satirizes the one topic above all others you aren't "allowed" to joke about.
For those interested I highly recommend watching it: https://www.dailymotion.com/video/x6shgvw
Decades later this all looks rather naive. The BBC, especially, could hardly make a program satirizing exaggerated concerns about child sexual abuse, given that the Savile scandal proved that many such concerns had in fact been taken nowhere near seriously enough.