Would studying in Ireland open up a few more doors when it comes to the job market, as it is in the EU, than studying in a prestigious British institution, such as Warwick? Now that the UK is cut off from the rest of the continent, I wonder what impact it's had on this.

I don't think there is a big change other than the long macroeconomic trend of Ireland overtaking the UK in growth and GDP per capita. I don't think recruiters fly to those islands to hire people from third countries to work in mainland Europe. Study in Ireland to work in Ireland,  and in the UK to study in the UK. In many industries Ireland is a more attractive market. 

That makes sense. I was already leaning towards Ireland, as in many senses, not to mention politically, it seems to be the better choice. 

Thank you.