Hi,
To both Teachittome and Blue USA, are you both US citizens currently and living in the US and wishing for a move to the UK?
If so, you'll find it extremely difficult to make the move. The reasons are that you'll need a job offer initially in order to begin the visa application process. There's plenty of teachers already within the UK, so it's not on the specialist 'skills shortage' list where those with specific skills are in high demand in the UK who then can have their applications 'fast tracked' as it were.
The above is a simple overview, there's a lot of great members here who know much more about the specifics and can tell you more.
If you are already in the UK, perhaps married to a UK citizen, then you'll find things easier as you'll already be on a visa that allows you to work - you'll need to 100% confirm this and there's many threads here about this along with specific information from the members I refer to above.
In short, if you are in the USA and have no ties to the UK that give you a good path to move over, then you'll find it's much harder to move here legally. It's pretty much the same the other way around, moving to the USA legally is very difficult too.
On top of all that, is the current turmoil with the government, the Brexit fallout and the fact that jobs and businesses are in 'limbo' as to their certainty, it's going to be difficult for the jobs market overall.
Hopefully, you'll both find routes to move over which you can realistically go for! else, I'd also suggest looking at other countries in the world to move to.
Cheers, DtM! West London & Slough UK!