Revd Gareth Jones has been suspended from his position at St Mary's Church in Ilford following the incident when he also kicked a police officer in the face.
The 36-year-old was discovered by medical staff passed out in his clerical clothes in the Covent Garden area, two weeks ago.
Highbury Corner Magistrates Court heard how he kicked a paramedic twice in the leg on Charing Cross Road before punching him and trying to bite him.
It's understood the Anglican priest told two intervening police officers he was protected by diplomatic immunity under the authority of the Vatican.
He admitted two counts of assault and must now pay more than £1200 in fines and costs, including £200 in compensation to each of his victims.
Revd Gareth Jones admitted consuming three bottles of wine, a cocktail of spirits and numerous pints of beer, and said he was seeking help for alcoholism.
A spokesman for the diocese of Chelmsford said: "We are deeply shocked by Mr Jones' behaviour. We suspended him from his duties as soon as we were notified of the incident.
"Now that the case has been concluded, we have started proceedings under the terms of the Clergy Discipline Measure. We are holding all those affected by this serious incident in our prayers."