The months terminal leave was nice, but you cannot be employed by 2 employers before commencement of terminal leave.
Just crack on with your new job. Your new employer will not give a stuff about the RAF regulations and will be more than happy to pay you for your work. If you have done what most people do you will have all of your annual leave saved up to the end, plus any resettlement you have left, plus your terminal leave which for me added up to 4 months, once you are out of sight of the RAF you are out of mind and they are very unlikely to come checking up on you! So start as soon as you can. Just make sure you keep enough back for the taxman as you will not be paying enough tax until you go back to having just the one job again.
Enjoy life outside, it's great!