Psychologist here although no longer working directly in MH services.
Nobody will be able to tell you for certain, but as a former supervisor of counsellors and assistant psychologists, I can offer this as a framework that counsellors must work to in services. Private practice may be a different thing, but I'm assuming you're looking at accessing counselling through an organisation here.
Safeguarding issues, or potential safeguarding concerns, in most cases, should be discussed openly with an adult client. Counsellors should not go and report something to social care without first discussing it with you in most circumstances, unless they had reason to believe there was immediate danger and you were refusing to cooperate - then they may have to override your wishes to disclose something to safeguard a child or vulnerable adult.
When considering safeguarding, the least restrictive option must be chosen and mental health professionals also need to consider the wider implications of making a report for the safety of the victim and their children in DV scenarios. We also have to assess if making a report where there is currently no immediate risk might actually increase risk because involving social services would alert an abuser who is attempting to isolate their victim that they are accessing services and possibly planning to leave - these situations are not always black and white. It is very likely that a counsellor will need to discuss your situation in supervision, but there should be something in the counselling agreement that covers that.
Based on the information given, your children are not in any immediate danger, they have not been seriously harmed or are likely to be seriously harmed by your husband, so there would be no grounds for overriding your consent and it is very likely it would be low on social care's priority list.
That said, a counsellor is likely to have to do a risk assessment with you that we call a DASH to gain further information about any risks to you and/or your children. They may encourage you to access support and input from other organisations or signpost or refer you directly with your consent. Women are often more at risk when they start making plans to leave, and just after they leave, and any counselling through NHS or charities will be time limited so I would strongly suggest accessing other support in addition so that you are not completely without it after counselling.
I hope that helps provide some reassurance and some sense of what to expect.