We've had the May Day holiday since the 4th century. Jim Callaghan tied it in to International Workers' Day in the 1970's. Now the Tories want to ditch it. Well not completely: they want to move it to October and rename it UK Day.
It more like they were itching to get rid of it for being linked with lefty causes. The reason actually given is to help tourism and extend the holiday season. In which case, why not both? We have among the fewest public holidays in Europe, and we tend to have them in quite bizarre places (why don't we have one in July when the weather is at its best?).
Another option would be to have regional specific public holidays like Spain do. We could have Yorkshire Thrift Day, where we demonstrate our character by not shopping and trying to make ends meet. Clogs are optional.
A UK Day is a stupid concept. Considering the United Kingdom has only existed since 1921, it doesn't seem worthy of a day of patriotism. And patriotism sucks anyway.