I have an article on Tyres from our local newspaper - it offered sound advice as does the RoSPA website. Question asked was one similar to yours - tyres not worn out, only done 'x' miles and not that old etc but recommended to change. Perceived wisdom is - check the tyre wall for any cracking/crazing- small or otherwise - usually along the wall not across the wall (although not unknown). Tyres do deteriorate with age. Check for any distortion on the tread or on the tyre carcass. Tyres that have been in storage should not be used if over 6 years old from date of manufacture, however if used this lessens the aging process but tyres over 10 years old should be replacedd irespective of the mileage covered. Chronological age of the tyre is found from the last 4 digits of the DOT code on the tyre sidewall, ie - 4702 is week 47 of 2002. If your tyre has a 3 difit code then it was manufactured before 2000 and should definitely not be used. If I was you I would check the age of the tyres, check the sidewalls for cracking/crazing, pop in to a local tyre place and get a second opinion, then make a judgement.
PS - I called in at the new Portsmouth centre at the beginning of July when in the area on business - not open then and looked a way away from being ready although with the distinctive OPC look about it. Clearly things moved fast if you have just had the car serviced there. Some of the techs are from OPC Bournemouth. Portsmouth site is a good central one adjacent to IBM North Harbour on a new Industrial/business park just off the A/M27 and fills a large hole in the OPC southern network. Should do well.