When did BR start running a relatively normal service on New Year's Day?
When I started at BR in 1982, there were no services north of Newcastle on NYD and the service between KGX and NCL was just every 2 hours routed via Leeds.
I recall both these (and generally restricted InterCity timetables), but I think it may have been a New Year's Day falling on a weekend (1983 was Saturday, 1984 Sunday), so the Monday was a public holiday in England and Wales (and the Tuesday in Scotland) with the result that the Sunday was exceptionally dead.
I think it may have also been tried on a 27th December when Christmas Day was a Saturday and 28th therefore a holiday.
I don't think it was normal every year. And people's travel, work and family situations have changed a lot since then - we rather took the restricted service for granted (but PLEASE don't let anyone get going on that hoary topic again, it's only March!)