Just as the title says. Is there any instances when someone from the UK has been denied a K1?

Yes. It has happened. The guy had apparently plead guilty of possession of marijuana whilst on a ferry, which atually turned out to be very bad. On his police report it said he was transporting illegal drugs internationally. No waivers could save him.

I'm sure there have been others, but that is the story I have read here on VJ.

But for people with no criminal history on both sides? I am just a little worried after finding out we are expecting a child.

I wouldn't worry about that! So long as you aren't criminals and don't have evil diseases, the odds are well in your favor! Relax and take care of your baby! Congratulations!!

I have NO statistics, but from anecdotal evidence - ie reading loads of threads here - I've seen many people approved when one partner is pregnant, and I don't recall seeing any denials
certainly not on that basis, anyway

sometimes people have to get a DNA test for the child, to prove paternity, but in that case it's about as strong a piece of proof of 'ongoing relationship' as you're ever likely to get