I feel you. It can be so hard to get a job here. Pretty much any UK work experience will look good on a CV. I also second volunteering to gain experience. You've secured a few interviews, so you're doing something right. Give it more time. I've had a really difficult time with finding a job (although, for a while I wasn't as proactive in the job search as I could have been). Conversely, I know another American who landed a job in her field after just a few months of arriving- with no prior experience here.
A few months after arriving, I volunteered and also worked in retail- just to gain some UK experience and to tide me over while I looked for a job related to my background. There is no equivalent job here to what I did in the states (worked for a government program related to both social work and education. I have a Bachelor's and also did some postgrad study), so the job search was tricky. You're fortunate that you have transferable skills! I was finally offered a job with a local college, but disappointingly the position was eliminated before I even started.
After that, I signed up with a few agencies. One day when I wasn't even expecting it, I got a call from a recruiter. She very quickly helped secure a temp job for me, and there is the possibility of it turning into a perm contract. It's doing administrative work, so not related to my background. But, I'm learning new skills and working with a really renowned organization, so that's great.
Have hope and be patient, it will come!