An English traditionalist bishop has incurred an unprecedented second excommunication by the Roman Catholic Church after consecrating a bishop without permission from the Pope.

It is the second time that Richard Wiliamson, 75, formerly of the anti-modernist Society of St Pius X, has been excommunicated. He was previously excommunicated in 1988 after his own consecration by French Archbishop Marcel Levebvre, founder of SSPX, which opposes reforms brought in after the Second Vatican Council.

Technically, Pope Francis does not have to do anything to excommunicate him this time because an illicit consecration incurs the penalty by default. Vatican Radio said today that he had been automatically excommunicated by his actions.

The society itself expelled Richardson after he outed himself as a Holocaust-denier in 2009 when he said he did not believe anyone was gassed to death at the Auschwitz-Birkenau Nazi death camp. He told a Swedish television programme: "I believe there were no gas chambers."

Shortly after Richardson made this statement, but before he was expelled by SSPX, the previous Pope, Benedict XVI, lifted his excommunication along with that of three other SSPX bishops with the aim of restoring unity between the society and the Catholic Church.

However, his dream of full communion was never realised. Two years ago the three remaining SSPX bishops rejected the Holy See's doctrinal proposals and Bishop Bernard Fellay, superior general, went on to criticise Pope Francis as a "modernist".

Bishop Williamson consecrated Father Jean-Michel Faure, 73, yesterday at the Santa Cruz monastery in Nova Friburgo in Brazil. Faure had himself been previously expelled by SSPX.

"The Society of St Pius X regrets sincerely that this spirit of opposition has led to an episcopal consecration," the SSPX said.