The P11D only applies to salaried employees.
One can set up a company and pay oneself through PAYE on a payroll system and then be subject to taxation on benefits in kind (form P11D - completed by your employer - er - you!).
However, one can be a "sole trader" or "proprietor" without a limited company (and all the hassles THAT involves).
In either case, if you put expenses through your business account which are for private purposes, they will not qualify for tax relief.
Therefore, if there is an element of your flying which is for pleasure (and why would it be - we all hate it!), both HMC&E and HMIT (Inspector of Taxes) MAY (only may) wish to disallow a proportion.
The P11D has nothing to do with VAT.
1 no. minefield opened up here!
Cheers
Whirlygig