Europe shuts down financial markets for International Workers' Day, so it makes sense that Ireland and the U.K. should observe this internationall recognized holiday in this fashion as well. While "Labour Day" is traditionally in celebration of blue-collar workers who work with their hands, society should show solidarity here, and that includes white-collar financial workplaces.
The United Kingdom and Ireland markets should close for a day of work as the rest of Europe does on International Workers' day. Not only would it unify Europe, this would come across as a sign of respect for all the workers within Europe, not just some parts of it.
I believe that it is unrealistic to close Stock Exchange markets for holidays. Many people worldwide participate in the Global Exchange markets, and by remaining open they are allowing those people to continue their jobs. It is not only good for the UK and Ireland, but for any person that participates in those markets.
The United Kingdom and Ireland shouldn't be forced to close their markets on May 1st. We have too many holidays as it is. If they want to work themselves to death, let them. Also if they want to estrange themselves from the rest of Europe by doing this, let them. It's a free world.
In Ireland, most businesses are generally closed on every Sunday, bank holidays and christian holidays. If you add that up it does take up a lot of days for workers to relax and whatever. Why even this Monday is a bank holiday Monday and nearly everything, except for maybe a few local shops will be closed for the day. And in the end, workers don't really feel like they need to be honoured. People work for themselves or their family to get money and live so it's really their own will and the regular runnings of life, not some big act of a saint.
I'm not quite sure about the UK myself but I assume they don't observe this made-up holiday for the same reasons, and they also have a bank holiday on Monday.