A church in London has come under fire after holding Friday prayers for Muslims last week.

St John's Waterloo held the event in partnership with the Inclusive Mosque Initiative. There are accusations that it violated canon law regarding only using authorised worship and Rev Giles Goddard, vicar of the church in Southwark, has been criticised for his closing prayers, which appeared to equate the Christian God with Allah.

Goddard read from Psalm 139, before concluding: "Allah, God, is always with us and around us, and is within us. And this is from the Hebrew scripture, so it is our shared, we all share, these great traditions.

"So let us celebrate our shared traditions by giving thanks to the God that we love, Allah, amen."

Executive secretary of the conservative Anglican Mainstream network Rev Andrew Symes said St John's had broken canon law, but added that it sent a wider message. He wrote that "inclusive mosques and multi faith services are not the actions of prophets but of poodles of the secular liberal establishment" and that the service would offend conservative Muslims.

He also said "this is not just an act of hospitality. Here Muslims are leading professing Christians in the worship of a deity other than the Trinity inside a church sanctuary. This is not merely an intellectual, theological and missiological question, or an issue of the flouting of church rules. It is, according to Scripture, something offensive to Christ who alone is worthy of worship and prayer."

The vicar has defended the decision to host the event, however, telling Christian Today: "We've been friends with Inclusive Mosque for a couple of years, and they've done some events here before. We host all sorts of things at St Johns – we try to be very open-play."

He said the church was "delighted" to host Dr Amina Wadud, a female professor and expert on Islam, gender and justice, who led the prayers because there is no mosque in London that would allow a woman to do so. "She's a great thinker...and well known in progressive Muslim circles," Goddard said of Dr Wadud.

People of all religions and none were invited to join in the prayers, which Goddard described as incredibly moving. "I think it's what the Church of England should be doing; encouraging people who are seeking to understand God more deeply in all sorts of ways."

Using the same language for God as Muslims shouldn't be controversial, he added. In Malaysia the government has forbidden Christians from using the term Allah, but that is what they call God. "We all understand God differently, but at the heart of both faiths is the belief in a supreme being who is love," he said.

"At the heart of every faith is the love of God, and the love he has for the world, and that applies equally to Islam and Christianity – they just have different ways of living it out. So it's a privilege to work with Inclusive Mosque, because they very much believe that God love everyone as they are, so human flourishing is at the heart of their faith, as it is at the heart of ours."

Churches should be promoting inter-faith unity "now more than ever," Goddard continued. He attributed the rise of Muslim extremism in part to the failure to form strong relations between those of different faiths.

"I certainly want to continue to work to develop strong and meaningful interfaith dialogue, to work to celebrate the things that bring us together instead of hearing so much about the things that divide us," he concluded.

"I think it's a small thing, but by hosting the event I felt we were able to take forward the sorts of dialogue we should all be engaging with."