You have to pay tax somewhere...
When I worked for Netjets I classed as a self employed contractor for tax reasons. I declared my earnings and after some deductions for running my 'business' I paid my tax and social security. All above board and very tax efficient, I made less money when they bought in the PAYE.
The problem is that some people don't even try to pay tax and then they get caught out. Hawkerpilot, I think someone at interview or indoc told you that your tax affairs were yours to sort out, we all have to pay some tax and I don't think your lawyers will get Netjets to pay your tax and social contributions for you.
Good luck with the job hunt...