Princess cruises are great and have several ships departing southampton july and august. hope you find one to fit your needs.
RCI's new ship Independence of the Seas is sailing out of Southampton next year and should be excellent for children. Also P&O new ship Ventura if you want to stick to what you know. Take a look and the RCI web site. Ventura has its own dedicated site.
Unfortunately RCI Independence does not do just a 1-week cruise next year - and it is also totally sold out of all 3/4 berth cabins for the July/Aug holiday season....very very popular.
I think the ocean villages sail from southampton, check there web site, hope this helps or just type in cruises from southampton, a page will come up with the ships.