Snigs,
I haven't worked as a flying instructor, but I was a one person limited company for some years. (I was a management consultant).
The advantages of a limited company are that you can pay yourself a very small salary (say £1,000), thereby minimising your PAYE liability. You then pay yourself the balance of your earnings in the form of company dividend, which is taxed at a lower rate. Thus, you can keep your tax liabilities quite small. You can also pay yourself reasonable expenses, which are not taxed. You must, however, keep good book records and prepare annual accounts for the Inland Revenue. The arrangement also has implications for National Health contributions.
The problem arises if you only have one 'customer' as appears to be your likely position. In this case, the Inland Revenue will definitely deem you to be in reality an employee and force the flying club to engage you as an employee and pay you a salary.
Thus, the wheeze of making you set up a limited company will only work if you actually do work for MORE THAN ONE club. I wonder if they realise this?
Remember also that being a limited company also has insurance implications. If you have an 'industrial' accident during the course of your work and you are incapacitated, who pays? Will the club sue you if your student is hurt in an accident?
Tread carefully, Snigs!
Very best of good luck,
BroomstickPilot.