I had low voltage with engine running - it basically was as if there was no charge.
I investigated the regulator etc and that seemed to be at fault - not putting out enough.
But before I bit the expensive bullet of buying one, I stole my wifes car battery - hey presto - all worked correctly.
Get you battery to Halfords and let them put their tester on it, just measuring voltage does not put the battery under load as the tester they use in Halfords will do.
It was a fault with the battery, though looked like it was the regulator \ lighting coil!
Easy fix and has been 100% ever since. I opted for a semi-traction battery that seems good for cranking\starting and good for running elcetronics as i don't have the need \ space for 2 batteries.
HTH
Rob