You have done nothing wrong. But it's two years four months since you bought the car so you cannot hold the supplier liable. The car is less than six years old and, as you say, Renault does not specify a timing belt change until six years old or 96,000 miles, whichever comes first, so you might be able to use that in an action against Renault itself, even though, in UK law, liability rests with the supplier. Law here: www.honestjohn.co.uk/faq/consumer-rights/

If this does not elicit a better response from Renault (50% of the cost would be a 'better response'), I would not recommend actually taking the fight to court. You have had two years four months use out of the car, so £3300 is fair depreciation over that period. So you should be looking at whether you throw away a car worth £5500 for maybe salvage money of £1000, or you investigate cheaper ways of fixing the engine. Talk to a local member of www.fer.co.uk/