Is there such a thing as wireless tv aerial connection?
 

Disclaimer: I suck at technology.

Is there a thing you can plug into the tv aerial socket downstairs, and into the freeview box upstairs, so the signal gets beamed up?

Or even better, can you get a plug in aerial like the olden days which will pick up freeview?

No

Just buy an inside aerial plug it into the upstairs TV and will pick up the freeview channels