Baxi boiler my kitchen tap has no hot water?

Hi, I have a problem with my Baxi boiler we get hot water upstairs only after running it for a while. but when we use the kitchen tap on its own down stairs it comes out cold there is plenty of water coming through the tap it's just not heated at all. The boiler doesn't kick in even if the tap has been on for a while full blast. We have to run the bath tap up stairs to get hot water down stairs.
The radiators seem to work ok upstairs and down.
Can anyone help please?