I'm almost sure that Irish car insurance policies cover driving in the UK as standard
And no need for a "Green Card"
But just to be sure check with your insurance company, it's probably on their website
It is compulsory that any car insurance purchased within the EU provides 3rd party cover in every EU country. There is no obligation for the insurer to provide Comprehensive cover in other EU countries, just 3rd party.
Most insurers also cover driving in the UK but it is worth confirming. It will be in your policy documents.