Unfortunately, as long as you don’t suspect that they are going to harm your child in any way, and your ex-partner has a contact order to see your children, then there is not much you can do. You can try to speak to your ex-partner about the situation, but they may not understand why you don’t want your children to see their new partner and this could cause more friction between you both.
If your ex-partner does not have a contact order and you stop them seeing their children then you risk your ex-partner going to court to obtain a contact order. This can be an expensive and lengthy process and the courts work on the premise that the child should have contact with both parents, unless there is a risk of harm.
If you think your child is at risk of harm from your ex-partner’s new partner then you must contact the police straight away. You may also be able to get an injunction against your ex-partner’s new partner if this is the case and they would not be able to see your children.