White privilege does exist. I personally think it is just overemphasised by more radical black people and underemphasised by some white people who are simply oblivious to it. Facts such as the under representation of black women in the beauty industry e.g. models, the disproportionate amount of black people being stopped and searched, driving while black, black people receiving longer sentences for similar crimes all point to a sense of white priviledge. One may argue that black people do commit a disproportionate amount of crime and that can justify my stop and search point, but that still does not give police a right to paint all of us with the same brush (ie criminals) due to the mindless actions of a minority of us.
That being said, I do believe that society in the UK is meritocratic overall. We do not live in a world where you are doomed to remain working class if you are not born white and where all white people are racist. Injustices do exist, but they should not diminish aspirations of the non white community. I am black and I'm doing pretty well (I'm a 1st year medic) so I believe that while white priviledge does still exist its overall influence on society is slowly diminishing.