I moved from Andover, but previously lived in London.
Some things are definitely cheaper, some more expensive. To be honest, you do not make the move for the money, as that seems to work out to be the samish in the long run.
I found that food shopping was something I really need to learn to do well. The general supermarkets are ok for basics, but fruit and veg is a real hit or miss and is definitely more expensive to buy good stuff than in the UK. In fact, I find that good quality food seems to be more expensive here than in the UK. You need to find somewhere you are comfortable with and has good quality stuff. You will probably end up with Costco for your bulk stuff, Giant or similar for your basics and Whole Foods or Wegman's or Trader Joes for the "nice stuff" and fruit and veg. I love Wegman's - you must find a Wegman's when you get a chance - or Trader Joe's.
We stopped doing the comparison with UK prices very quickly - or you will drive yourself nuts.
With regards to schools, Tyson's is too far for me to give good advice. But I am not sure you want to live there. Traffic is bad and I have not noticed any nice neighborhoods, although they may be hidden. I would consider Reston, McLean, or Great Falls, or come to Sterling - we love it here. You need a good realtor to help you through the process. Ours was worth their weight in gold!
You can start by looking at greatschools.org - it is not perfect, but it gives you a starter for 10. You will need childcare and private schools until they are 6 - they do not start 1st grade until then. If you find a good school with a kindergarten class, it will likely be half day.
I have been very happy with the childcare we had for my ds since we got here. When we first arrived, he started with a chain called KinderCare - it is a franchise and as long as you chose carefully, you can find very well run ones. He has been in 3 different ones while we settled in - we moved to rental and then bought a place. He is now just finishing 1st Grade in a local school and has done really well. Be prepared for a LOT of parent's involvement in school - much more than you have ever seen in the UK, but it is nice. He is starting with afterschool care at his Taekwondo dojang in 2nd grade, and is very excited about that. They pick them up in a limo. 
The biggest difference you will find is that if you live in Fairfax county, your smaller kids will start school later in the day.
Loudoun county starts earlier in the day for grades 1-5, then a little later for middle school and latest for high school. Fairfax County reverses that - which we do not believe makes sense: teenagers are heading for the bus at 6.30am, but the smaller kids need to go into childcare even before school, so mom & dad can go to work. At least my ds only goes into childcare after school.
Join the Living in America thread, everybody is nice and helpful. I have not been on there as much recently, but do not be afraid to dip your toe in.