Lil some EPUs are walk in, but you'd need to check on their website. I don't think many are open at the weekend, though, and as far as I know most A&Es won't do scans but will refer you to EPU.
I hope you get to see someone asap and that everything's ok. Have you noticed any pattern to the bleeding? Is it after you've been exercising / active?
I think the first trimester is by far the most stressful! One you can feel the baby moving, it's so much more reassuring! Although DD had a bloody strong kick and I used to be able to see her toes through my skin! Ack.