I've been thinking some more about this, because although what I said was honest, it's probably not very helpful to you.
So, I thought, if I were working in your job and so had to do something, what would I do?
Here's some suggestions. With the caveat that these need to be offered, not pushed, and if any family chooses not to take advantage, that is in no way a cause for concern. I would suggest the most appropriate way of making HE families aware of these things would be a website where they are listed.
Are there ways for HE children to be able to join in with intra-school activities, e.g. music service/ county children's orchestra (if there is one)? If not, why not, and can you make arrangements?
Can under 16s join in with any adult education courses offered in your area? For safeguarding reasons, they might need to be accompanied by a parent, but otherwise there should be no reason why not.
Do the LA ever run competitions for school children (e.g. "design a recycling poster" - you've probably seen the sort of thing)? If so, what are the arrangements for HE children to be able to enter? What happens if they win (particularly if some/ all of the prize is resources for the school)?
I reiterate that not all families will want to use these services, but some may.