I have to seriously question the sanity of this plan.
The last troops had only been pulled off Dunkirk on June 3rd. While the situation was not quite as dire as some of the movies have made out, the British Army had been utterly decimated, had lost virtually all of its heavy equipment, including 45,000 soft skinned vehicle, ~850 anti-tank guns and 700 tanks of various types. There was enough equipment in the British Isles on June 5 1940 to fully equip two Commonwealth divisions, one of those was the Canadian 1st ID which was recently arrive in-country. Montgomery's 3rd ID has been part of the Dunkirk evacuation, it had rifles for all of its troops, but had virtually no trucks or other heavy equipment worth mentioning.
The British command, while not defeatist overall, DID seriously worry about a German cross Channel assault at a time when the British army was a force with firepower closer to 1880 than 1940 standards. To take HALF of the equipped Army forces on Britain and try to invade what was likely going to be a fairly unhappy Ireland would have been way beyond idiotic, it would have been criminal.