Something's Invaded My Sprouts and Purple Sprouting!

Never grown these two crops before but they have both been under fine mesh netting ever since I planted them... BUT I have an infestation.  There must be millions of the things... every time I touch a leaf a small flurry of white, almost luminous (quite pretty, actually  ) flying things take to the air before landing back down on the leaves.  There are patches on the leaves everywhere which I presume are the eggs.

Does anyone know what they are?  Also, how could I have prevented their arrival and now they are here, does this mean my sprouts and purple sprouting will be wiped out?  Is there any treatment, bearing in mind I'm reluctant to spray chemicals on there?

I'm attaching photos and, as usual, many thanks for your advice.

Floody

Difficult to tell from the photos but they sure look grey and that means mealy aphids on the leaves. Maybe there's a few whitefly on the net as well. ... I've had some mealy aphids appear on my PSB this week, and a few weeks ago on my sprouts. No matter, the same treatment as DBG said, still applies.
The best way to avoid big infestations is spray the early arrivals, and keep doing it a few times. They soon get the message. A nice strong well directed jet from the hose is also a good answer. I'm sure PSB and sprouts positively like the strong fresh jets of water.
If you don't get rid of them, they will cause your plants harm by smothering the new growth. They are fairly easy to get rid of, then look out for new starting colonies and do the same. Mealy aphids tend to arrive in numbers a lot quicker than the whitefly who often take a couple of weeks to really get any numbers settling on the underside of leafes. The larger plants recover quite quickly as if nothing happened.

I don't know exactly but the soap makes the bugs slip off or suffocates them - so just  couple of squirts of soap to a litre of water will do the job

Thanks for the replies.  The hosepipe isn't an option and I just can't find the time to go to the lotty every day.  Think I'll let 'em have a free rein this year and try to catch 'em early next year...