I've been through this. Remember that the wilder the allegations he makes, the more credibility he loses (my ex said DD was covered in bruises and continued to allege this while a doctor and social worker were looking straight at her and could see it wasn't true). It is really not unusual for an ex to make these kind of allegations. The claims have to be investigated, but that doesn't mean they are going to be believed.
Get yourself organised. Have one file where you keep evidence that you are the primary parent - as sea says, ask school/nursery to confirm if you do pick up and drop off. Write down if it is you who brings them to the doctor/dentist and any activities. Keep a diary that shows who has put them to put them to bed, changed nappies or whatever (I don't know how old they are). Even though it's still your word against yours, the diary still helps to portray the care you give to your dcs, stuff that you might forget to say if you are in a meeting with a social worker or someone.
In a second file, keep any evidence of his abuse, whether it is in the form of texts/emails he sent or a record of contacts you have had with WA, NSPCC and others. Write down all the past instances of abuse you can remember, with dates if you can.
All this information is useful in any investigation, but it can also help to prevent you from spiralling into a panic.
I'm surprised that you wouldn't get legal aid if you went to a refuge, for example - can you double-check this point?
The professionals involved are very, very aware of the possibility of false allegations by a malicious ex, particularly one is wants to get residence of the dcs. Keep calm, cooperate, do your utmost to get away from your ex, and you will get through this.