This is an approach that's been suggested to me before - work out how much you've spent in total on repairs, divide it by the number of months you've owned the car. If that figure is say, £150/month, then this repair is about 15.3 months worth. Given the condition of the rest of the car, if you think you can reasonably expect not to have to do anything else for 15 months then it's worth it.
IMO though, if £2300 is going to fix it properly.. what else are you going to buy for £2300?