Hi there.
Yeah, Kayak.com is usually the place I go to first. June is a tough month, since you're in the summer season - but usually you should be able to find something around $900.00 per person. (My family usu. flies out of SFO - and I've done it many times). Also, check
airfarewatchdog.com - sign up and get their alerts for SFO international travel. Kayak's alerts are okay, but they don't seem to be very timely. Airfare watchdog also has a co.uk site, but it's not quite as 'on the ball' as the US site.
If your family can begin their travel the last week of May, you'll find significantly cheaper fares. I think the days of finding $300 airfares to London are gone.
I'm constantly trying to find the cheapest fare. My DH & I are planning a trip back to Oregon sometime in March (need to clear out my house and try to sell it).
Other sites to try 1800europe.com, if all you need is cheap fare, and don't necessarily want to earn airmiles..
Ummm, that's all I can think of right now - but if you find something, let us all know!
Lisa