Sorry for being a Pedant, but I don't think there is anything called a Visa waiver scheme in the 'excited kingdom'.
The term comes from the Americans where all nationalities (save the Canadians) require visas to enter the 'excited states'. A large handful of Europeans and a smaller handful of Australasias have this requirement waived, under certain circumstances. i.e. coming as a tourist, knowing what moral turpitude is, promising not to be a member of a communist party.
For the UK there is a list of nationalities that require visas, everyone else does not require one.
I recall one of my first flights into Heathrow in the late '70s. Came in on Pan Am from Seattle (No BA flights then from YVR, AC less than daily) and was confronted with three queues; UK citizens, Commonwealth citizens and 'Others'. Since I had arrived from the US about half the pax went to the UK queue and nearly the other half went to the other queue. Only I went to the Commonwealth queue joining passengers off of Air India and PIA jumbos. Now that took over two hours too.