The letter, addressed to the conservation director Bill Martin, is damning of the state of the quango.
'I am not leaving English Heritage because I am depressed or defeated, but I fear I will become so if I stay,' the letter states.
Heath's resignation comes in the aftermath of a series of major cuts at EH in the light of funding problems. The latest tranche came last week (Cash-strapped English Heritage forced into major cutbacks).
A statement from EH said: 'We are saddened that David has chosen to take a very personal line on budget restraints that are being felt by everyone across English Heritage.
'It is well known that since the '90s EH's grant in aid has not been increased in line with inflation. Since 1997 our grant in aid has reduced in real terms by £16.7 million. Despite our long-term programme of efficiency savings and modernisation it has been necessary to make further budget savings.'