Tiny white bugs killing my banana plant....?

I'm now on my second plant after loosing the first to these pesky little things. On the first plant (Sid) I didn't notice them until it was too late, I tried pesticides, warm soapy water etc but the damage was just too bad the the leaves and the poor thing didn't survive. The bugs also infected my... show more I'm now on my second plant after loosing the first to these pesky little things.
On the first plant (Sid) I didn't notice them until it was too late, I tried pesticides, warm soapy water etc but the damage was just too bad the the leaves and the poor thing didn't survive. The bugs also infected my orchid which after several treatments was free from them but the underside of all the leaves had a white tint where they were damaged by the bugs eating them. I guess as the orchid has thicker waxy leaves the damage wasn't so bad as it looked. No other plants in the house were affected thankfully.

A year on and we have bought a second banana plant (Sid 2) and I have put it in a bright window and been keeping a close eye on it expecting to see these bugs again. Nothing, until this morning when I noticed them on the underside of two lower leaves again. There were hundreds of them and they make a kind of random web. This time some were brown and some white, I guess the white ones are the mature ones and the brown the young?
If I left them they would cover the whole plant (18" tall 5 leaves) in a couple of days and there would be the web between the trunk and leaf stems and between the underside of the leaves and the tips where they curl down a bit. The bugs are no more than a millimeter long and I cant even take a photo of them with Macro on my camera they are so small!
I have just sprayed, gently wiped, re-sprayed and left the plant with Bayer Garden Provado Ultimate Bug Killer. There are sitll a few bugs crawling around so I have re-sprayed again.
Once the sun goes down I'll give it a REALLY go spray off with a hose pipe in the garden and then re-apply the bug killer.

So anyway, what the hell are these things and how can I beat them for good?! I refuse to lose another plant to them!!

Thanks in advace :)
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