Heat sealing very thin polythene

Cheap way – careful use of hot knife (quickly, do not linger at a spot) will work if you have a hot knife.

Spinnaker or kite double sided tape will also work but is much more expensive. Less fancy double sided tape would probably also work.

You could try a sewing machine if the plastic is not too flimsy. I tried this recently with polychro and was very pleased with result on test material

I recall seeing a battery-powered bag sealer in my local 99p Store. It had a heated element, and you ran the bag through this element. It's quite a common technique; the element is usually a wire over what appears to be a woven glass fibre strip, with a mating strip above.

I'd look in kitchenware departments…

I'm going with double sided tape, after a messy excursion with the silicone gun. Thanks for the suggestions.

For future reference, perhaps:

Portable Heat Sealer, £1.82

Can’t vouch for its efficacy, mind…

Google did the job.

Thanks Kevin, trying to use it to do 22' of airtight sealing might be a tad frustrating I feel.