You could possibly try to sand the floor with a special type of sander called a ''square buffer'' It is very non invasive, and you can use a super fine(150-220) grit sanding pad.
I wouldnt really recommend this as it will probably take off at a min 1mm of the veneer, but if you are absolutely in a pinch you could use it carefully with good results.
Do not under any circumstance substitute a drum sander for a sqbuff. It will chew through the veneer faster than you can say 80grit. If you can find it a random orbit sander will do the job also, just make sure you stay above 200 grit papers, and youll be ok.
You can find these tools at your local rental centers, but I wouldnt know where to begin in the UK.
One other option is to cut out and replace the worn section of flooring with sometype of inlaid design. Stars are popular, as well as circles with intricate designs. You can buy these prefabbed on the internet, and you simply cut the old floor out and glue down the new inlay. Presto new floors, that very well may raise the asking price for your home.
Hope this helps.