Broken timing chain on BMW with N57 engine

Recently the engine on my 3 Series Touring stopped dead. A trip to the BMW dealer revealed timing chain failure, and I have a bill for around £4000. I can't pay this at the moment, so I am without the car until I can!
The car has always been dealer serviced, is a 57 plate and has about 160K on the clock so technically high mileage I suppose.
I became aware of problems on the N47 engine, but was informed mine is N57 and the same problem doesn't apply.
I've made BMW customer service aware that I am not happy with their refusal to accept any responsibility. Their argument is that I should have taken out an extended warranty.
I'm currently trying to ascertain whether the timing chain would have been covered by an extended warranty, and also how much that warranty would have cost me.
I understand that the timing chain is fitted at the back of the engine, and is inaccessible without removing the engine. On this basis how can it ever have been checked for wear, and as other commentators I have read have said on this basis, BMW must have taken the view that this part would never need servicing access.
I believe that BMW should cover some of the cost of this since clearly the part has failed. Otherwise BMW are saying that their parts can only be guaranteed for three years. Not what I expected when I set out to pay £39000 for a car.

Asked on 24 October 2015 by Jem Wilsher

Answered by Honest John
The car is eight years old and has done 160,000 miles. BMW now has a programme to check timing chain tensioners on dealer serviced N47 and N57 engines back to 7 years old and 120,000 miles but your cars is just outside that limit. In fact, in the UK no 'supplier' or manufacturer of anything has any responsibility for it beyond a reasonable 'life' of 6 years and if a judge heard that the engine has done 160,000 miles I think he is unlikely to hold BMW liable for the failure.
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