The history of healing being used as proof of a monarch's divine right is well known in England. It looks to me that there is a correlation between the extent and enthusiasm of the practice of the Royal touch used in the healing of 'scrofula' (presumably a variety of skin diseases including tuberculosis) and the validity of the King or Queen's claim on the throne.
(The same test is found in the Lord of the Rings, where Aragorn's claim to the throne of Gondor is confirmed by his unique ability to cure the fatal disease caused by the Nazgul's 'black breath'.)
After all, by touching 'the people' the monarch is breaking a powerful class taboo (only those of noble birth were typically allowed to touch the monarch, therefore royal servants were usually upper class; such as the ladies and gentlemen 'in waiting').
And more importantly the King is setting himself up for the possibility of public failure; because if the touch does not produce the beneficial effects which people expect, then the monarch's authority is undermined.
It is significant that the most popular monarchs, and those most sure that their authority was indeed divinely ordained, have put themselves to this public test repeatedly; while conversely, those whose authority was arbitrary - such as the Dutch William of Orange, or the Hanoverian George I, have refused to try and heal the people; on the grounds of the King's Touch being an absurd superstition.
Apparently, the formal practice was introduced in England by the first of the Tudor's, Henry VII - whose reign came at the close of the destructive Wars of the Roses; and it reached its peak under the Restored Charles II, following the Puritan Republic.
After later dying-out (significantly, Charles II's brother the ineffectual and deposed James II disliked the practice); touching was reintroduced by Queen Ann (James II's daughter) - one of the most popular and effective of all British monarchs.
Anne took touching seriously, fasting on the day before. One of those she touched was Samuel Johnson - the greatest intellect and scholar of his day, and a deeply religious Anglican; showing that this was not merely an ignorant superstition.
Indeed, the patterns of its usage and disuse suggest that it is reasonable to assume that the Royal Touch worked, when performed by the legitimate monarch - at least by normal standards of proof.
Consequently, the test and practice may come into its own again in the future - if a new claimant to the throne of Albion were to present himself or herself to the people.
(Of course - if the prior assumption is made that healing by the true King's touch is impossible - then any success will simply be explained-away. But the evidence is strong for those who have not pre-decided the issue.).
Added note: It seems likely that the healing touch is inderpinned by love - more than anything else. The love of the monarch for the people, the trusting love of the people for the monarch. That isn't the whole story - but a necessary element.