In the early years of the War, the medics might have rejected some. By the summer of 1917, the British Army was in desperate need of reinforcements following the ravages of 1916 and with new carnage, such as Passchendaele. This encouraged a policy of recruit now; examine later. And then, if a man proved unfit for trench warfare, there were plenty of non-combatant jobs to be done.
The RDC (Royal Defence Corps) comprised 27,000 men who were unfit to fight. Half of them were guarding PoW camps. There was still plenty for them to do following the armistice and it would be April 1919 before some were discharged.
Research by David Ball, Ringstead