Boris Johnson and Jeremy Hunt are going head to head in the first live hustings for Conservative leader.
The pair are the final two MPs vying to see who should replace Theresa May as party leader and prime minister.
The politicians took turns to make a short speech, followed answering questions posed by journalist Iain Dale and then from members of the audience.
Speaking first, Johnson refused to answer questions about why police were called to his home in south London following reports his partner could be heard screaming.
He insisted the Conservative party membership had not come to the hustings to hear about it and spoke about his promises during his tenure as London mayor.
Dale repeatedly pressed the point, saying: "You have just taken up a minute with that answer which answers absolutely nothing".
He said the issue is not just a private matter as the public has a right to know about things that reflect a candidate's character.
Johnson responded were "people (were) entitled to ask about (his) character" but "when (he) made a promise in politics (he) delivers" and spoke about his successful project to deliver routemaster buses in London.
Police were called to the flat Johnson shares with his partner, Carrie Symonds, in Camberwell, south London in the early hours of Friday morning when concerned neighbours said they heard a woman screaming and smashing sounds.
"The caller was concerned for the welfare of a female neighbour," the police said in a statement issued on Friday evening. "Police attended and spoke to all occupants of the address, who were all safe and well."
"There were no offences or concerns apparent to the officers and there was no cause for police action," the statement said.
In his speech to the party membership, Johnson has called for the UK to leave the EU with or without a deal and says his vision for a modern Britain is under threat from a Jeremy Corbyn government.
But Hunt said they need to renegotiate a new deal and says the first thing he would do in office would be to set up a new team which would also contain members of the Scottish Conservative party and the DUP - the Northern Irish party which is proping up the minority government.
He said the UK had to avoid having a new general election before Brexit is sorted and proposed new measures such as cutting UK corporation tax to "Irish levels" so he could park "economic jumbo jet on Europe's doorstep so they need us as we need them" when negotiating a new trade deal.
When answering questions from the audience he supported children learning about LGBT education in schools he said his closest friend at school had come out as gay on their last day of school.
He said his friend had been keeping it like a dark secret and he thought no children should have to live like that.