Polo 1.2, 2013 plate, timing belt broke a day after major service?

Hello, so my Volkswagen Polo is about 6 years old with around 47k miles on the clock. I have just sent it in to an official Volkswagen garage where I have brought several cars off them and done all my services. I spent around £300 on the major service and the day after I received it it wouldn’t start and it turned... show more Hello, so my Volkswagen Polo is about 6 years old with around 47k miles on the clock. I have just sent it in to an official Volkswagen garage where I have brought several cars off them and done all my services. I spent around £300 on the major service and the day after I received it it wouldn’t start and it turned out to be the timing belt or chain. VW have said it’s not our problem and we need to pay the £4,000 in repairs. What can I do because surely they should have checked and or seen in diagnosis that there was something wrong when doing the major service?

Any advice would be appreciated, and any questions I will answer.
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