No, no, no. This was a show called 'Incredible Games'. It used to be on BBC1.
Freak, you're correct that the kids had to keep going up in a lift. It had lots of little games - similar to Knightmare Doolallygirl - but these were much more sillier. For example, the pool game was basically an alphabet soup game. In the pool, there were lots of letters and the person in the pool would take each letter to their partner and try and spell really long words.
It was 'hosted' (the guy who was The Lift) by a certain David Walliams, now of 'Little Britain' fame. Comedy genius!