MBP keeps restarting over and over again

My MBP 15 (circa 2012) keeps restarting over and over again and never gets to a user login screen. The flow is: power up > see logo and progress bar > progress bar gets near end and screen goes grey > screen goes black and machine restarts > repeat

I have tried booting to safe mode and this just goes to a grey screen that hangs. After 30mins + I have to manually power down as nothing appears to be happening.

I have tried to boot to recovery mode - this went to logo with progress bar and then to a black screen (backlit so I know power is on) where it hangs and nothing appears to be happening.

I have tried resetting the SMC but this has no impact.

Any thoughts on what to try next?

By way of background - I am on High Sierra (latest or latest -1 version), have no external devices, and the MagSafe power cable is plugged in and showing a green light)