From a legal perspective, yes, of course they can forward your details to Social Services without your permission. It is not a breach of GDPR.
From a safeguarding perspective Beavers are spot on.
One of the issues with detecting child abuse is that the signs are rarely clear cut. Most of the possible indicators of abuse also happen with children who are not being abused. For example, a child soiling themselves is a possible indicator of abuse, but most children who soil themselves are not being abused. A single indicator on its own is, therefore, meaningless. However, a pattern of indicators means there is something to investigate. It still doesn't mean the child is being abused but it means the possibility must be seriously considered.
In this case we have a boy aged at least 6 poking other children in the genitals. Like it or not, regardless of the circumstances, it is a possible indicator of abuse.
If agencies such as Beavers don't report this kind of thing, Social Services have no chance of detecting possible abuse. If you read the report of the Victoria Climbie case, you will find that many agencies failed to report signs that, on their own, were capable of innocent explanation. Had they reported these signs it is possible Social Services would have realised she was being abused and taken steps to protect her.
Neither Beavers nor Social Services think you are a bad parent who needs help. I would be surprised if Child Services actually contact you. As this was an isolated incident I expect it will be filed and forgotten. Eventually the record will be destroyed.
As someone who is involved has been involved in child protection in a voluntary capacity for many years, my view is that Beavers have not in any way over-reacted. They have treated this incident correctly. It is, sadly, the case that far too much abuse still goes undetected because youth organisations, schools, doctors, etc. fail to report incidents like this.
For clarity, I am not in any way alleging that your child is being or has been abused. As with most other indicators of possible abuse, most children who behave in this way are not being abused.