Katie [F] barre the door!

Practice til it hurts. When you play an E chord do it with middle, ring and pinky. Barre that 1st finger over. You may have to bring your elbow in towards your body a bit more and make sure your thumb is right in the middle of the back of the neck. Now practice. A lot!

Q: "Is anything really made up of zeros and ones??"
A: Redheads!

Keep reminding yourself that once you get this barre sorted you'll be well placed for B and then barre chord playing in general. It can still be hard switching between barres and open chords rapidly. But once you've got it you'll find yourself sliding up and down. So a G/F shuffle is just a matter of moving the shape two frets. Obviously you don't want to keep shooting up and down the neck but I see some players do it (check the YouTube for Johnny River's Mountain Of Love).

Redheads are typically gorgeous...or not. A 10 or not. Or in binary 0110 or not.

You could also try raising the neck higher so the frets are easier to get at.

One other thing no one has mentioned naolslager is to be sure your thumb is positioned to give you the best leverage. Move your thumb and wrist around a bit till you find that sweet spot where your forefinger has the most power with the least effort 

You can also start with a 4 string version of F ( XX3211), before you graduate to the full barre. It means you can play tunes with an f and still practice the full barre.