I'd wash first as it will lift any small loose plants as well as dirt. then when dry you can spay the weeds. use something like Pathclear as it has a long term effect.

Alternatively if you use the weedkiller first you'll have to remove the dead moss etc which could leave bits of soil on the paving which would be annoying if you'd just washed it.
Be aware that you shouldn't pressure wash block paving as it tends to remove the sand in between the blocks.

If you need to use a spray on algae killer its best not to wash afterwards because it takes a while to be fully effective.

Horses for courses really. They won't interfere with each other chemically. Sorry not to be more help.

Thank you.
Sounds like it's best to clean first, then use weed killer, maybe a few days later.
I will report my findings later in the season.
Just hope the weather plays ball and the rain lets up for a while !

Wait, hold the phone! I don't think using this broadcast method of weed killer is the best idea. You don't have much control of where it goes unless you just want to kill everything in sight. Keep in mind that the weed killer will remain active in the soil for months and you won't be able to grow anything. The season is shot this year. You also have to think about aerosol drift. Where will the wind carry it? You may incur lots of unintended damage. I'd recommend using a separate spray bottle for the weed killer. That way you can use it precisely were you need it without all the collateral damage.

depends on the weedkiller Paul. Many on the market in the uk become inert on contact with the soil and Marge is cleaning a block paving patio so she isn't spraying the beds with it. Pathclear prevents anything else growing which is why it is formulated for paths in particular and yes you don't want that on the flower beds.
But it is wise to do this on a still calm day to prevent wind blown drift as you suggest.

Two separate sprayers, one for weedkillers and one for other, less noxious substances are always best. But I always apply Pathclear with a watering can and a fine rose - that way, it goes only where I want it to, no spray drift.

I understand Eileen thanks for the explanation. I just felt that with a spray bottle she'd have more control and less run off.

You can get a rose for a watering can designed for weedkillers. Instead of a round rose it has a bar with lots of holes so you can control exactly where the weedkiller goes. Many weedkiller instructions show you two different dilutions, one for spray and one for watering can.

Wow thanks everyone for all the good advice. Seems like quite a lot to think about before I start.
Especially as I have two large areas to smarten up which will take some time.
Oh well that's life !!