I am on the other side of London from Kentish Town but this happened to me last night with my daughter (4). Myself, my wife and our two daughters (7 and 4) had been at a church ceremony and then a related event at a friends' house a few suburbs away which had run a lot later than we expected (partly due to World Cup viewing). We don't have car and it being a Saturday night minicab and Uber availability/pricing were not good. So we got a train back and then had 5 minutes to walk from the station to our house. We needed to pick up milk for the morning so my wife and 7 year old went into the 24 hour shop beside the station. This was about 11.45 p.m. I had the length of our road to walk, that's all.
My 4 year old was not happy about walking and was crying a bit (very tired as you would expect after having been woken up after a sleep on the train, but it was a 5 minute walk and really there was no better alternative. She is 23 kg so too heavy to carry the full distance (I already had a backpack). She wasn't running away or anything like that. I was in a suit and shirt because of the church ceremony.
About five houses away from ours two 20 something women ran up from behind us, grabbed my daughter and started shouting at her asking whether I was her daddy. As you can imagine, she went completely hysterical. I told them to take their hands off my daughter or I was going to call the police. I said we lived four doors away and had lived here since before my daughter was born. The commotion was such that the people in the house we were in front of, who know all our family, came out and told these women that I was my daughter's father.
At this point, I just walked to our house went in, and put my daughter down. My wife witnessed the commotion from the other end of our road although she didn't know that it involved us. She walked past the two women walking the other way and when she got home and I filled her in she told me that she recognised them from a house on our road that was recently bought by the council divided into flats and rented out and said she regularly sees these two women outside smoking - which might have been what they were doing when they saw my daughter and I. My wife said that she's pretty sure that neither of the women work (my wife is a SAHM) and don't have husbands/partners of their own.
We live in a fairly mixed area. If we had been a few streets away where it is all £1.5m houses of City professionals like ourselves this would never have happened because 90%+ of children in those houses are being raised by married mothers and fathers and there is nothing strange about a father being on his own with one or more children. However, statistics show that among the white English lower income group (which these two women were from) 65% of children under 16 don't have their father living with them. So they see a man with a child and they think they can barge in and try to grab the child off him. From the posts here it's very obvious that it's a class thing among English people. Upper-middle income fathers much more likely to be on the scene, lower income fathers not so much. Also, although not related to what happened to us yesterday, for families like ours it's completely normal for my daughters to preference their mother over their father especially when they are tired, stressed or looking for comfort. I work 65 hours a week so that my wife can be a SAHM - a choice that is more hers than mine but which I am happy to support. They hardly see me from Monday to Friday.