In this case the OP has asked for "avoiding crowds" and "possibly less crowded options". If somewhere such as Westminster Abbey requires tickets then you are not, by definition, achieving those aims.
At Westminster RC Cathedral that is managed by adding additional masses.
I have very deep and fundamental theological problems with a requirement to have tickets (even free ones) to attend a religious service, let alone to scramble for them weeks ahead- in this case I gather 3 weeks before Advent has even started.
I'm far from certain that it isn't even against Canon Law.
As such it would be a real turn off for me to go to such a service, as I deeply don't consider it is matching the first and basic principles of a Church.
A Church is there for the pastoral requirements of everyone, pastoral requirements which are just as acute at Christmas as at any other time (maybe more so).
There are other solutions- as I say add extra services or open up St Margaret's (the sister Church to the Abbey) and stream the service in, or maybe other measures (stream it outside?).
A religious service is NOT a sports match, or a Taylor Swift concert- if you feel you have no option as a Church other than to ticket, either do that 24 hours beforehand or even on the door. Apart from anything else that might actually suppress demand- from those who don't want to queue.
Personally I prefer St Paul's worship to Westminster Abbey (but that is a personal thing)- at St Paul's I have actually been to services largely in Latin. At Margaret Street there was also one service (on the Wednesday of Holy Week) with significant segments in Greek. For anyone who attended such services were "a language understanded by the peoples".
At my own Parish Church we struggled deeply with the idea of ticketing for Christingle as demand way exceeded our fire certificate. We eventually decided to add a second Christingle service.
Even in Central London there are many other Parish Churches (real Parish Churches) beyond the two I have mentioned, and also Royal Peculiars. I don't know if the Peculiars all have Christmas Day services- but St Peter Ad Vincula in the Tower of London, the King's Chapel of the Savoy and the Guard's Chapel all spring to mind- all really interesting places in their own right. Yes the public can always attend services at all of them- at St Peter ad Vincula without Tower admission tickets. I guess they would have a service- there for the resident warders.
The Churches I have mentioned (and there are many others) are actual parish Churches with a proper resident Congregation.