Here we go again, having to explain the obvious about the fact that for multinationals there's a competitive market in taxation.
You attract business by having lower tax rates. If you're a country's finance minister you have to work out whether that's a good thing to do because your local businesses pay the same take rates as multinationals. If you have a large economy of local businesses lower tax rates mean you bring in less taxes. You might attract some big multinationals but their taxes won't compensate for the losses.
If you have a small local economy bringing in multinationals is a double win. The multinational taxes more than cover the losses from local businesses so you're in the black and the lower tax rates help local businesses become more profitable. Having a small local economy means either having a small population for that economy to support or having a larger but impoverished population.
Being in the EU there's no legal reason why we couldn't lower our CT rates to compete with Ireland or Luxembourg - after all, those two are also EU members. If we'd tried it in the past HM Treasury would have been greatly out of pocket because of the lower tax take from local businesses and VAT and/or income tax/NI would have had to go up and I'm sure you'd have complained about that.
You could, however, be right about our having greater freedom outside the EU. Remember that the precondition for making money from multi-nationals is to have a much smaller local economy and if the population size doesn't change that means they each get poorer. Are you quite sure that's that you want to do?