I shall be interested t hear what they say about corruption in the UK but I suspect that, comparatively speaking, there isn't much. Politicians and government departments may waste zillions on new computer systems, for instance, but it's mostly down to incompetence rather than corruption.
However, though we don't have to bribe anyone to get basic medical services, you do get better ones if - quite legitimately - you pay for them. I'm never sure what exactly makes that different from paying a bribe, from the point of view of the person who has to pay the money.