@DilemmaEmma2 I work in this area. When social services receive a referral like this, typically they will check their own records and ask the police for information (as well as other relevant agenices). The police share details of convictions, but also intelligence - including (but not limited to) how many times they've had contact with the individual either as a potential victim or perpetrator, markers for things like suspected or proven stalking/harassment/violence/weapons, if they've been subject to marac etc. All of it is taken into account because it's all evidence of risk (of course a decision has to be made about how good the evidence is, but as a previous poster said if we have several ex partners who have been alleged victims of DV that the police have been out to, we don't quibble over whether it resulted in convictions) Children's services will look at whether he's known to them including when linked to other children, eg with previous partners.
Childrens services can't share the police information with the partner, but typically they may say that he cannot be around the children and if he wants to be, they need to risk assess it and see if it can be done safely or not. They usually encourage the partner to do a Claire's law disclosure, but if they don't and the concerns are serious enough, they can request that the police go out and share the information.
Children's services don't have authority to tell people to split up. They can say that someone isn't safe to be around the children, and that the relationship can only be separate from the children, until some work is done to make it safer. If it's not possible to make it safe enough (like the example someone referenced about a woman moving in with a guy who was a sex offender) they can say that it's so serious, we will go to court to seek removal of the children.
Domestic abuse and sexual abuse are two areas where there's a huge gap between harm/risk and conviction levels, so it's always about what we realistically know or suspect to be true rather than what has been through the criminal courts.