Re: Still not sure why any of this is an issue
They can't simply invoice from Ireland and avoid UK tax. They must in fact be an irish company that is invoicing from ireland, and ultimately be the company that the buyer contracted with. There is very little stopping you from setting up an Irish or Luxembourg based company and doing the same thing.
If the UK wants to attract more tax revenue then it needs to reduce its tax rates.
Tax is a marketplace - companies will do business where conditions are favourable.