Our car was registered new in March 2016. We bought it on 25 Apr 2016 from Arnold Clark with 9 miles on the clock.
On Friday evening my DH was driving home from work when it went into 'limp mode'. It went to the Mazda garage today. First DH was told £95 + vat to diagnose what's wrong. They then phoned a little later and said that was inconclusive as the engine was loud and further tests were needed so it would cost £330 (not sure if incl or excl vat).
They phoned not long ago telling my DH that the oil pump chain has snapped causing scoring and the guide for the chain has broken. This has caused big end bearing scarring. We need a short engine and gaskets and it will take 24 hours labour which will cost £5,533.47. 
I know it is just out of warranty but the garage said even if they phone Mazda that is all they will say. He also said Mazda won't cover it as they haven't done all the services (they have either been done by Mazda or Arnold Clark and we have receipts and service records).
We just don't know what to do. Are there any circumstances where car manufacturers do pay for work just outside the warranty? Anyone know our legal position?
Surely there must have been something wrong with the chain before the 3 years/60,000 miles warranty expired? (We have 64,000 miles on the clock).
Any advice? - we're totally shell-shocked.