I'm not familiar with Spitfire wiring, but here's a general checklist for sussing out electrical issues such as this:
It's highly unlikely that you have multiple issues bringing down multiple components.
Start with the battery. Is it charged? Is the alternator charging with the car running? If no, charge battery and address alternator issue.
If both check out:
Look at your wiring diagram and find where the offending components share commonality: A common ground, a common switched power source, a common fuse, etc. Then check at that common point. If a ground, is it clean and tight, no corrosion? If not, clean ground point and connector and reconnect. Apply some dielectric grease to help keep the corrosion at bay.
If a common switched power source, check for power to the switch and then from the switch. If power in but no power out, bad switch.
If a common fuse, check the fuse. Even a fuse that doesn't look blown can have corrosion on the contacts preventing it from flowing current.
That should get you on your way to figuring out where the problem lies, at least.
Robby