There is a scheme through BA at Swanwick. Go to the "London Control online" page on the intranet and there is a Fam Flight page there.
I have organised a few through the BA contact (PM me if you need details) and they have been a massive help.
The only major problem is that I have to do them in my own time and at my own expense. Whilst the novelty factor of the first few made this worthwhile, I have no desire to go on any more if I have to foot the bill and use up my leave.
I really want to go on more fam flights, especially something different such as trans-atlantic or with a smaller bizjet operator but I have no idea where to start in trying to organise something. The company don't seem one bit interested in assisting with the organisation or accommodating them better, which is a pity.
Controllers NEED to spend more time in the cockpit and pilots NEED to spend more time liasing with ATC in order to gain a better understanding of what each of us do. The fam flights I have been on over the past year or so have been absolutely invaluable for the knowledge I have gained and the pilots involved told me that they gained a lot from it too.
It's a pity that management won't acknowledge this.
EDIT: It see that someone is claiming something is in the pipeline. Fingers crossed it takes off (ho ho)!