KLM uk was the brand name of a British airline subsidiary of KLM, which operated services within the UK and between the UK and the Netherlands.
KLM launched the brand name “KLM uk” in 1998, when KLM acquired majority ownership of AirUK.
In 2000, KLM uk launched Buzz, a low-cost subsidiary. Buzz was sold to Ryanair in 2003, at which point the remainder of KLM uk operations were merged into KLM Cityhopper.
Source: Wikipedia