If you know where you're moving for sure I would contact the LEA (local education authority) in that area. I am sure you can find their number online by searching for the community's govt. agencies. The authority can tell you what schools are available in that area. It would be good to let them know you're definitely moving mid-term so that you can find a placement. Right now there are several communities here that are having a hard time placing children for next year.
My twin sons started out in reception this past Sept. As a former middle school teacher in the US, I was a bit concerned about them starting full-time school at such an early age. I was especially worried because they just turned five a bit ago, making them the youngest in their class. They have managed brilliantly though...in fact, tomorrow is their last day! (The school calendar is one aspect of british schooling you will have to adjust to.)
I have been supply teaching 12-16 year-olds quite regularly. I can say that from my experiences here, the schools are not more educationally demanding than the US school I previously taught in. I am sure your children will fit in fine at their ages. I would go ahead and look into available school placements for them right away though. Knowing the name of their school will be helpful with their adjustment.
Good luck!
Just found this site, I haven't looked at it, but it might be helpful:http://www.dfes.gov.uk/studentsupport/students/lea_lea_contact_det.shtml