You probably can - but if you are used to being quite honest you might find it difficult!
I believe that job seekers allowance entitles you to 6 weeks to find a job of your choosing before you have to start accepting what they give you (there are a lot of minimum wage jobs out there!).
People obviously do play the system - have an interview get the job and make sure you are sacked 2 days later and voilą - another 6 weeks of dole being the most obvious.
And in order to claim the allowance you must be able for work (ie not training on several days a week). If you are going down the route the fact that you are self funding a very expensive training course doesn't hold any water with them at all - don't mention it and pretend you are an unemployable moron.
As to benefits other than job seekers you could try your local citizen's advice bureau