Stefan, for a lot of people the price of a new washing machine is beyond their means. It's finding that lump sum that's the issue, even if it's not a particularly expensive model.
Not everyone has access to credit either.

There are a whole lot of struggling people out there who don't qualify for tax credits to help bump up their meagre wages because they don't meet the minimum working hours criteria. Underemployment is becoming a real issue in this country.
These people often get forgotten, but I would imagine it's very difficult for them to save up £200 or so for a new washing machine.

It might not be particularly economical to pay a launderette to do your washing but some people have no choice.

I've worked with many of these people and I know the daily choices they have to make and they are simply unable to save up - that would be a luxury.