I've had this argument with them before. Oh, the rules have probably changed now, but last time I was out of work I got their stupid little form to fill in and found that it wasn't big enough.
So I got a spreadsheet. Labelled it all nice and simple so even DWP employees could understand it. Filled it in with absolutely everything I'd done in a fortnight; everything. Three pages of phone calls, visits to potential employers, emails to agencies and companies....
If they want to take the p!ss out of me, I'll take the p!ss out of them by doing exactly what they ask for... to a stupid level of detail.
By the way, if you're getting it at all consider yourself lucky. I applied in December; I got a letter from them a month later after emails and phonecalls asking what was going on with my claim. 'You have applied for contribution based JSA. However, you have not paid enough NI in financial year 2011/2012.' Fine, I thought, they'll put me on income based. Oh, but that's what they used to do. The letter went on.... 'and you are not entitled to claim JSA because you have said your partner works more than sixteen hours per week.'
Yep; they've changed the rules so you can't get basic allowances if you haven't paid enough NI and your missus is working full time. So the DWP are, in essence, saying that whilst you've paid taxes and NI to the government to supply services and a support system when you need it you won't be getting anything.
Thing is... they changed the rules. They didn't change the law. So with absolutely no shock at all I made some discreet enquiries with friends who have a legal background.... and the DWP rule changes are illegal because they are not backed by law.