I would definately get onto your local council website then to see if they have any care work positions.
Get onto local jobs site/paper to see what they have.
Also see if any organisations around you help with that kinda thing and whether they advertise jobs or whether they use agencies that specialise in that area.
Have a look on yell.com for local job agencies and see if any of them specialise in care work. You can register for several agencies and still apply for jobs.