I think what people seem to be missing in this is that he attended the parents evening, then a letter regarding the situation was hand delivered to the Head of Governers and the following day when she did not attend school the police arrived.
My strong feeling is that someone who recognized him and knew about his past attended the parents evening and wrote to the governers to warn them. When she did not attend the next day the school would have been concerned she was home alone with him which is why the police attended.
I've come across similar while working on projects which involved social service cases. I would be almost 100% certain that SS will become involved and that there will be the potential for removal of DD if the relationship did not end.
The best advice given on this thread was that given by a police officer which I'll repeat because it was so good:
Another police officer here. He isn't telling you the full story im afraid. He wouldn't serve 4 years for assault on a pc plus for Claire's law to be read to you he most definitely would have been convicted on domestic assault. It sounds like it was serious and that there is concern for your safety. I second asking for full disclosure of his previous offences. Speak to the police and not your partner about this and protect yourself and your child.
OP I think when you see the police you need to make a Clare's Law application as a matter of urgency. I suspect if you do they will give you information on his previous convictions there and then and you will probably get a nasty shock.
You say that your partner is really nice and caring. There is a method of grooming families for abuse which is called 'love bombing' and involves making victims feel so safe and cherished and loved and cared for that when the abuse starts they don't quite believe it or think it is out of character and so tolerate it. It sounds like this may be going on here so don't be fooled by thinking 'but he seems so nice'.
Looking at your previous posts you do seem like a bit of a vulnerable family who have a few problems and you've been very lonely and really wanting to find a partner which makes you very vulnerable to someone without good intentions. It's extremely early days in your relationship and you seem to have got very involved very quickly including involving him with your children which is a bit of a red flag.
I agree with other posters who say that you need to end this relationship. It seems to have so many warning signs it's untrue. Is this the man you wrote about recently who doesn't talk to you but just watches TV and doesn't want to get physically intimate? You met him on the internet?