We had a nasty round of whitefly in the greenhouse which got to the chillies and everything else, and was eventually solved with two rounds of application of something containing Imidacloprid (which I recognise in another, veterinary, guise, and so should you!). You're allowed two applications per growing season for food crops.
In your case I recommend evicting the basil from the greenhouse, since it's nice and frost free outside anyway, before treating it. This will achieve two things - reducing the risk of infecting your chillies, and hardening off the basil plant to make it less attractive to the little blighters in the first place. I wouldn't be surprised if you ended up treating both with nasty insecticides, though, I'm afraid.
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In your case I recommend evicting the basil from the greenhouse, since it's nice and frost free outside anyway, before treating it. This will achieve two things - reducing the risk of infecting your chillies, and hardening off the basil plant to make it less attractive to the little blighters in the first place. I wouldn't be surprised if you ended up treating both with nasty insecticides, though, I'm afraid.