I know that gannets aren't rare, but for a beginner birder like me, who hasn't seen a wide variety of birds like most of the people here have, that's what I consider rare, because those were the only ones I've seen as a beginner birder. And I just want to clarify that I was asking about what birds occur in the UK that are considered "rare" but that's my fault for not making that clearer.
I still consider myself a beginner.
However the rarest I've seen would be Greater Yellowlegs! I'm lucky that it's been only 20 mins from me for a couple of weeks now, and that's a biggie. I went to visit a couple of times and one day it wasn't showing and everyone was asking each other if it had been seen and everyone was saying no, and I felt so bad for people that had travelled so far, I stayed for hours longer than I would have just to try and help them find it! haha there were people from Edinburgh, Skye, Newcastle, Glasgow!
Also, at the same place (RSPB Loch of Strathbeg) and same week, I was lucky enough to see Lesser Yellowlegs, Pectoral Sandpiper and Little Egrets.
Other than that, I still consider things like Snow Bunting rare! I've only seen them once.
Even Long-tailed Tits I get excited about when I come across them in the park once in a while. Or Greenfinches! I
rarely ever see them in my local park, which I'm in every day. And Siskin I've only seen maybe two or three times in the park. And this is over a couple of years.
What's common to some people, isn't always common to others. And it wasn't too long ago that I was pleased to see my first Gannets! Even though there's a major breeding ground just 30 miles away