I've restarted the campaign by accident, can I cancel this?

Having finished Borderlands 2 core campaign I closed up for the night, when I restarted it presented me with the option to start in "True Vault Hunter Mode". I misclicked and now I'm right back at the start and my friends are all in Sanctuary laughing.

Is there a way to cancel this campaign restart?

Can I connect to my friends games and continue with the DLC as we planned?

You haven't actually restarted the campaign, you've started playthrough 2. However see How to get to play-through 1 after starting vault hunter mode? for information on how to get back to playthrough 1. But you haven't lost anything and will probably want to play playthrough 2 with your buddies instead of continuing playthrough 1: see How do subsequent playthroughs work? Long story short, you'll only get better guns and a decent challenge at this point by playing playthrough 2.

Your current playthrough progress doesn't affect your ability to join friends games though; even if your friends are in a different playthrough or part of the story you can always join their game (the only risk is enemies may be impossible/crazy easy if your levels are mismatched). You can even hop into a DLC campaign you haven't started via a friend (only if you own the DLC of course)