It's difficult to find real specifics of their rules and lockdown.
What they have in place currently with vaccine passports also allows a negative test or proof of recent recovery to enter non essential businesses.
For the lockdown of the unvaccinated in place now it says they can only leave the home for essential things which is pretty much how it already was as far as I can see.
The big change is the proposed fines next February for those who don't get the vaccine. How they would police that is the question.
As a comparison Canadians aren't allowed to enter the same places without a vaccine passport. They also can't use a negative test or proof of recovery so that's more restrictive than Austria
They also can't use trains or planes domestically and I don't see any restrictions on that in Austria.
I think the term lockdown does need to be clarified in these cases
I'm personally against all of these measures but if you ask if it should happen in the UK then what specifically are you referring to?
If you need a vaccine passport for non essential businesses is that a lockdown?