fox
My musings-
You need to be looking in the places that part-time work is advertised, you also meed to consider that by restricting the type of work you seek to office work, and then restricting the hours you want to work will obviously reduce the number of jobs available to you.
Are there any other restrictions - are the times you want to work fairly set or can you be flexible, is the salary you want achievable, how far from home are you prepared to travel, are you rural with limited workplaces in that area or central?
So consider are the limits you are placing on the job you want too restrictive and if so where can you compromise?
Then are you looking in the right places - have you done an internet search for any jobs in your area, local papers, jobcentre, word of mouth?
Is your CV up to scratch (and how have you explained the circumstances in which you "lost" your last job), have posted it (or if skint walked round hand delivering it) to local employers pro-actively asking if they have any work or can they keep you on file, have you looked on gumtree/advertised yourself on gumtree? Have you registered with the big employers - I know the civill service has a website that you can register for notifications of any jobs coming up in your area, does the NHS, your local council?