The fact that the UK calls public holidays "bank holidays" is the most adorable quaint thing you guys do.

Anyway, there's some nuance here. I think the Wikipedia section for the UK on "international worker's day" says it quite well:

A public bank holiday in the United Kingdom known as May Day was created in 1978 and is held on the first Monday in May each year.

There are many traditional May Day rites and celebrations, some of which have been held for hundreds of years. However, it was not until the late 20th century that May Day in Great Britain became linked to International Workers' Day, and the holiday is not officially a "Labour Day".

If they called it Labour Day, that uppity working class might think they have some kind of value.

/s