pics hijacked from here https://www.howacarworks.com/basics/how-the-starting-system-works
One way or another, you've got a problem with the solenoid sticking. Try tapping the solenoid with a hammer - even if it doesn't work, it will make you feel better!
The Bendix has an external solenoid that may be mounted anywhere between the battery and starter.
The Bendix drive (gear on the end of the shaft) suffer from the grease getting old and thick "glueing" the gear to the shaft instead of letting it slide. This results in the starter spinning up, but not engaging.
The "Pre-engaged" starter integrates the solenoid to switch the current only after the drive gear has engaged, but it includes an over-run clutch to protect the starter once the engine has started.
My guess is you have the "pre-engaged" type (lucas M45 or M50?) and the solenoid contacts are welding. With a few tests to confirm, replacing / rebuilding the solenoid won't be your most difficult job.