As a lot of us find out when we retire, once the Military has your ID card and your forms are all filled in and signed, their interest in you disappears. If you start another job it will be classed as a second job until your service finishes officially, for obvious reasons, and you will be taxed accordingly. Example - my tax and NI allowances are with my pension, so any earnings on top of this are fully taxed, it all balances out in the end.
I also know of guys that have attached their resettlement to their terminal leave and started their offered employment.