I would see if you know of anyone who does academy games at these clubs.
If not, then see if Birmingham does have any connections with the clubs mentioned. You could contact your RDO even if there is nothing on the website, and see if he knows how to get onto the clubs.
If any of the above doesn't work, then go to the club. Although, you could go to the club first. I went direct to the club, as I knew they had no connections with my LFA. But, there are many contacts at my local RA, which I wasn't part of before I began. The guy that appoints for the club attends that RA, so would've been able to speak to him there if I had been there.