Vigils are taking place across Ireland and the UK in memory of murdered 23-year-old teacher Ashling Murphy. Irish police are continuing to hunt for the killer of Murphy, who was found dead on Wednesday after going for a run on the banks of the Grand Canal in Tullamore, County Offaly. The Garda Síochána said it had made “significant progress” in its investigation amid reports that detectives had identified a person of interest. Gardaí said they were not releasing details for operational reasons. On Saturday afternoon a large crowd gathered in London to pay tribute to the teacher. The vigil took place at around 4pm – the time at which police said the fatal assault occurred. Attenders queued to sign a book of condolence and lay flowers in Camden Square, north London and a minute’s silence was held. Vigils are also due to take place in Edinburgh, Glasgow and Brisbane. Earlier in the day parkrun runners in the Republic of Ireland, Northern Ireland and beyond held moments of silence on Saturday morning for Murphy. Hundreds of people also gathered in Cork on Saturday morning for a vigil, with more planned in towns and villages across the weekend. Thousands of people gathered in the late afternoon in Tullamore, Dublin and Belfast on Friday, as Ireland continues to reel from the murder of Murphy, with echoes of the national reckoning that was sparked in the UK last year by the murder of Sarah Everard. Events also took place in Belfast, Dublin and other towns and cities on Friday. Murphy’s family attended a candlelit vigil near the murder scene on Friday evening. Her father, Ray Murphy, paid a poignant tribute to the talented young musician by performing her favourite song, When You Were Sweet Sixteen, on the banjo. The taoiseach, Micheál Martin, has said that the murder has “united the nation in solidarity and revulsion”. “No stone will be left unturned in terms of bringing this investigation to a completion and to bring the person responsible for this to justice,” he said on Friday. Michelle O’Neill, Stormont’s deputy first minister, said at the vigil in Belfast: “I think the sheer fact that, right across every town, village and county across this island today, people are gathering in large numbers to remember Ashling Murphy shows that women have had enough. We are entitled to feel safe, we are entitled to be safe. We are entitled to go for a run. We are entitled to go to work and feel safe, we are entitled to go to the shops and feel safe. I think this is a watershed moment in our society today.” The death of Murphy has sparked fresh debate about the safety of women in Ireland, with many asking how such an attack could happen in broad daylight. “We, as a society, need to face up to this. There is an epidemic of violence against women. It’s been going on for millennia, quite frankly,” Leo Varadkar, the deputy prime minister, said on Friday.