Finding a Job with a Licensed Employer

I'm currently aiming to find a job using the Tier 2 - Skilled Worker category of immigration (because it has lower thresholds for maintenance funds and is less expensive to apply for), and will start my search with companies who are already Licensed Sponsors under the Tier 2 Register of Sponsors. I found the register of sponsors here:

http://www.ukba.homeoffice.gov.uk/sitecontent/documents/employersandsponsors/pointsbasedsystem/pbsregisterofsponsors

I think it is updated fairly frequently--this one is current as of today!

If I find an employer on this list who will hire me and issue a certificate of sponsorship, then I don't have to go through the process of persuading them to become a License Sponsor with the UK Border Agency in the first place, which I hope will be easier.

There don't appear to be many companies registered in Birmingham (mostly local government, universities and sporting agencies), but if nothing pans out there, I'm hoping I can find a company registered elsewhere who may need to hire someone for there Birmingham offices, or for a remote position. Working from home is an option, but I'm really hoping to have a physical work-place so I can actually meet some new people and get out of the house at least a few days a week.