On Sunday, 30 June 2013 18:17:51 UTC+1, MrWeld wrote:
A relative has about 80m² of gravelled areas around their house. Over
the years, the gravel has become very muddy, and is now coverered with
weeds.

Is there a cost effective way of washing gravel? I've tried putting it
in a handheld steel sieve sloshing it around in wheelbarrow of water,
but that was very slow, and generated large quantities of muddy water.

I suppose I could just put a membrane on top of it, followed by more
gravel, but I'd like to re-use the existing stuff.

Gravel is a cheap solution to create a hard surface and will always be a problem. The mud has likely come up from underneath due to a poor job to start with.
Usually put down immediately before selling a house to "tidy up".
You can do what you like, it will be as bad again in a couple of years.
You need to be thinking of another solution.