My non-biometric UK passport is pretty worn too. The wording and crest on the front are totally gone. There are numerous stickers and marks all over the cover pages too. The inside pages are dirty from so many thumb marks running through it. I've never had a problem with it in all my travels and I still have another 5 years of validity so it will get worse.
As long as the picture page is readable (both by human and machine) and there is enough room for any stamps or visas you may need there is no problem.
I have heard a passport control officer at Eindhoven airport telling a UK traveller that his passport was on the verge of being refused, although the passport was falling apart at the seams and was missing the front cover from what I could see. That is the sort of state it has to be in to cause any trouble.