There are exceptions - the Midland Main Line and Paddington closures for example (I think you'd struggle cutting off major commuter towns like Reading and Bedford from their direct route to London for a week or so at
any other time of year) - but generally I'm inclined to agree with
@AlterEgo that Boxing Day services could work if there was desire from industry and Government for it to be done and that it's a separate argument to Boxing Day's near-complete shutdown on the mainline network outside of certain geographical areas currently in any case. You absolutely could have extended closures over Christmas and run trains around these on Boxing Day, like is being done every other day in the week between Christmas and New Year (not inclusive).
I'm not thinking we'd ever want to be running close to a full service - mid-morning startup time and Sunday0frequency services with Christmas Eve-esque early shutdowns would be fine in my view as the end goal to aspire to, which would get those who wanted to travel where they needed to be - if conditions are right and it's funded appropriately, I can't imagine there not being the volunteers to run that level of service.