If you've joined BHPC, you could try posting on the forum [if you haven't done so already] and ask Alan Goodman because he used to/still might do race pedal cars as well, so he might be able to point you in the right direction, or somebody in that community that knows of such sites.
As for other web sites - there are lots of small bits all over the place. Depending on what material you're looking to use, you might get something from general welding sites, or general carbon fibre sites as well as dedicated bike sites. It's a case of drawing all the strands together. And I can guarantee, after you've built your first one, before you've even ridden it, you'll probably be thinking how you can improve the bike and you'll be thinking about the next build. That's what happens down rabbit holes
edit: For example, I was looking at this chap and his Kingcycle Clone the other week [don't ask me how I ended up there]. I've not met the gentleman [he might even post here], but I think he is/was a member of BHPC. This is my sort of builder......easy come, easy go. And it's the most forgiving was into building something - heavy mild steel and a basic mig welder. What's not to like
https://www.youtube.com/watch?v=tKPDR6za3t8&t=979s
