In reply to aln:
I haven't, but a colleague (who lives in Bellshill) has been doing this since last Autumn; she has found it quite lucrative as a second job, and fairly easy to fit around her working hours (09:00-17:30 five variable days a week).
I think it depends where you live, and on the time of year - it'll probably be really good during the run-up to Christmas.
By 'business tax for your car' do you mean business-use insurance for your car? I think Amazon provide that as part of the deal, though it's probably wise to also check with your own insurer in case there are complications.
She knows other people that do it as part of a mix of different delivery jobs (e.g. Hermes), that probably complicates insurance.