As others have touched upon, I think it's down to a number of things but mostly the rise of the half marathon. I've regularly run half marathons for several years and friends and family always ask me if it's a "full marathon" despite me saying "the Bath Half" or "Cardiff Half". I think people have adopted "full marathon" to help avoid confusion but also to add some gravity to the distance for non-runners.
I know nothing about football but have many friends that live and breathe the sport. I make no claims to even pretend to know much about football, but friends do appreciate when I make an effort and ask them about various facets of the sport and they're always careful not to nitpick when I've made too grand an assumption. I'm equally the same way with them when they ask about running. I'm a self-confessed running bore and do my best to subtly correct people when they've made a mistake regarding halfs, fulls and distance, e.g. if they called a half marathon a "full marathon", I'll just say "13 miles in a half is my optimal distance. I can run the 26 miles of a full marathon but would have to seriously train for it." Nobody thinks I'm a pedant and I've managed to educate!
A few of these have been mentioned before, but just think of them as universal London Marathon truths!
Book a table in advance for your dinner on Saturday. Eat when you want to, not when a restaurant can fit you in.
Get up earlier than you originally think you'll need to. Being early is fine and if you're running late, you'll then simply be on time!
Stop drinking with about an hour to go before you start so that you can visit the loo and stay empty. Take a bottle of water or energy drink for the first couple of miles to compensate for not drinking before.
Take a bin liner, not to wear but to sit on. The grass in the blue start area was wet with dew last year.
Make sure you and your family/friends are very specific about where they will be on the course. You won't have the mental energy to keep searching the crowd for their faces if they're not where was agreed.
Avoid the Lucozade gels given out unless you've tried them before. Carry your own preferred brand instead.
Pack a pair of flipflops or fresh, comfortable shoes to change out of when you finish.
I was in a similar situation in last year's VLM where I'd put down an estimated time of 4:10. After a solid year of committed training, I managed to bring my spring half marathon time down to 1:37 so a 3:30 marathon was realistically on the cards. My pleas to be promoted up to an earlier pen fell on deaf ears both in the lead up and also at the expo.
I was shoved into pen 8 out of 9 with most people looking to run nearer 4:30, so I knew I had a lot of work to do in the early stages. It was like running a gauntlet where I struggled to maintain a constant pace, slowing and speeding up to squeeze through gaps etc. Following the blue line was completely out of the question until Canary Wharf where people started dropping like flies around me.
Sadly from about mile 21 onwards, I started to run out of steam due to my earlier struggles. I eventually crossed the line in 3:52. A friend of mine had been shoved into pen 9 and managed to beat my chip time by about a minute going through a similar experience.
Long and short of it is it's possible to a run a decent time even if you've been placed too far back. Don't fight the crowds early on and go with them. When it thins out, that's when you should make your move and try to hit target race pace. Don't needlessly waste mental and physical energy speeding up and stressing out about the slower runners around you during the early stages.
The only club I can think of off the top of my head that are based in the city centre is the newly formed Birmingham City Striders. I believe they meet in the Jewellery Quarter on Tuesdays and Thursdays at 7pm.
If you're willing to travel further out of the city centre, there's BRAT as others have mentioned that meet at Birmingham Uni and Bournville Harriers. I've also run with Kings Heath Running Club before and they're a friendly bunch, too.
All of these places are fairly easy to get to using the bus network and all should only require one bus to get there from the city centre.