Earlier this week, and not for the first time, neighbours of Chrissie Chambers and her children were disturbed by a commotion. As they tell it, they could hear a furious altercation. The police were already on the scene. Eventually, shots were heard. When police entered the house, they found Chambers and her youngest child, two year-old Shania, dead. Chambers's ex-partner, who was also the child's father, was taken to hospital with such severe injuries to his face that police have been unable to question him. An older child had escaped through a bedroom window.

This was the grim drama played out in a street in Braintree in Essex. And while it must be assumed that the rights and wrongs of what took place will one day be examined in court, three possibly pertinent claims quickly came to light. The first came from neighbours who said they had seen Chambers beaten in the street by her ex-partner on several occasions. The second was that, also according to neighbours, Chambers had lodged repeated complaints about harassment by her ex-partner, including more than 100 threatening text messages she had received. He was also reported to be subject to a non-molestation order. The third was that a court hearing was due later that day to consider arrangements for parental access to Shania.

Now the violent killing of anyone, let alone a mother and her child, is – thankfully – rare enough in Britain still to be treated as news. The same is true of the killing by a parent of his or her child. And such killings fall into quite distinct groups. There are mothers, more rarely fathers, overwhelmed by the demands of caring for a child who is disabled or particularly demanding. There was the case of Fiona Pilkington who killed herself and her daughter, Francecca, after years of harassment and taunting by youths on the estate where they lived. And there are mothers who kill their offspring while suffering acute post-natal depression.

But there is another group, too, and one that seems to be growing – though it might be just their often sensational nature that gives these cases undue prominence. This is where one parent kills before what they anticipate will be an unwelcome custody decision. This was the motivation that emerged in court earlier this year, when Theresa Riggi, an American who had broken up acrimoniously with her oil engineer husband, admitted stabbing their three children to death at their Edinburgh home. As the court heard, she opposed her ex-husband's claim for full access and had done everything she could to prevent them seeing him. The custody hearing had been fixed for the following day.

Just weeks after the Riggi case came to court, Christopher Grady was convicted at Birmingham Crown Court of murdering his five year-old daughter and attempting to murder his six year-old son, by driving them at speed into a freezing river. He had picked up the children from his estranged partner one day last year, telling her: "You've got 10 seconds to say goodbye to your kids, and then they are dead." He had regular access, but – it appeared – had become increasingly resentful. The Independent Police Complaints Commission decided the police could not have prevented what happened.

Also last year, Fiona Donnison turned herself in to a police station in East Sussex, saying that she had killed her children. She led police officers to her parked car, where her two young children, a boy aged three and his 18-month-old sister, were found wrapped in bin-liners in separate sports bags. They had been smothered. She and her husband had split up three months before, and the separation was marked by furious arguments, including an allegation of assault. Like Riggi, Donnison had made an unsuccessful attempt at suicide.

Cases of this sort, of course, are not peculiar to Britain. One especially heinous example earlier this year concerned a Canadian father of twins who abducted them from his ex-wife's home in Switzerland and is presumed to have killed them, before throwing himself under a train in southern Italy. Whether or not such tragic crimes are really becoming more frequent – or simply coming to light more often – they share so many features that it is surely worth asking whether more could not be done to prevent them.

The killing of Chrissie Chambers and her daughter raises two distinct questions. There is the perennial one of whether the police are assiduous enough in their response to complaints of domestic violence. The IPCC has already launched an inquiry into this particular aspect. And, to give the police their due, campaigners concluded last year that, in general, such complaints were being treated more seriously. Nor is domestic violence as straightforward an issue as it sometimes looks with the benefit of hindsight. Women may be reluctant to come forward or withdraw complaints after they have made them. There are difficult dynamics here. Which is not to say that much more cannot be done.

The other aspect relates to highly charged custody disputes. With family break-up now almost commonplace; with some parents prepared – as they have been since the beginning of time – to use children as weapons in adult quarrels; and with fathers less resigned than they once were to losing custody, all the ingredients are there for bitter parents to resort to desperate measures. In the most extreme cases, this may entail killing the child to prevent what the "losing" parent anticipates could be something "worse".

It can hardly be coincidence that the eve of a crucial court appearance appears to be an especially dangerous time. This makes the argument for custody decisions to be much speedier than they are and for court-ordered access to be far better enforced. But it also suggests that the police should be alerted to the timing of custody decisions when one or other parent is known to them through reports of domestic violence. In some cases, this knowledge might make no difference; desperation breeds diabolical deviousness and extreme actions. In others, though, a custody dispute plus a history of abuse might tip the balance in favour of police intervention – or, as they say in international affairs, activate the responsibility to protect.

m.dejevsky@independent.co.uk