NiceBiscuits Firstly, you need an appliance engineer, not a plumber. Also, are you sure you need one? My neighbour had the same problem and her DH (who had broken his leg and pelvis so couldn't get down on to the floor) told her to go and buy this gadget to tighten something or the other, she did that and all she had to do was tighten something and her dishwasher started to drain again. Do you have any neighbours etc who are handy with this sort of thing? I'm in Lewisham too, and completely useless with things like that too. Do have a handyman's number you can call up if you are desperate?
If you google the dishwasher brand and model and the problem, I am sure you will be able to fix it yourself! (P.S. I did that the other day when my laptop threw up an error and fixed it myself! I am no IT genius either...)
I recommend A1 Grafters from Lewisham they are in ladywell I think. They do all my plumbing and do waste disposal too with a large truck. They are very well recommended in Lewisham even with the councils own website I believe.I have used other plumbers in the past and been ripped off but this company are totally honest and very fair with their prices.