How can I clear a slow running kitchen drain?
Get a drain cleaning water bladder of appropriate size for your pipe.  They should have them in the UK.  They are readily available in the US and Canada. Hook it up to a garden hose.  Take off your kitchen sink's trap (the U pipe) and feed it as far as you can into the drain pipe.  Turn on the water to the garden hose, and it will likely clear out whatever you have in there.