Er, Tboo's answer seems to be back to front!
Irrespective of whether there's a warranty in place or not, your statutory rights in respect of a faulty item are with the
retailer, not with the manufacturer.
Your statutory rights are effectively divided into 3 periods, viz:
1. Pre-'acceptance'
2. Pre-'6 months'
3. Pre-'6 years'
I wrote in detail about your different rights during each of those three periods, here:
http://www.theanswerbank.co.uk/Law/Question527 308.html
Your situation is that, if you can show (based upon the balance of probabilities) that the most likely cause of the problem is an
inherent fault (i.e. poor quality components or poor workmanship during manufacture), the retailer is obliged to repair or replace your washing machine. (You can specify which of those options you'd prefer but the retailer can substitute his preferred option if your choice is not economically viable).
Short-life 'expendable' components are not covered by your normal rights. (e.g. you couldn't buy a car and expect the retailer to replace the wiper blades for up to 6 years). I doubt that a washing machine pump would come into this category but I'm not a 'white goods' engineer so I don't know how long they should reasonably be expected to last.
This might also be of interest:
http://www.theanswerbank.co.uk/Law/Question526 691.html
(It might be worth searching online to see if a broken pump is a common problem with your model of washing machine).
Chris