The job centre wants four months of bank statements to make sure they're not overpaying me. I've had about £800-£1500 a month coming in on top of the dole from selling my old crap on ebay and the bank of mum and dad giving me dosh. Would they consider this as a source of income?
Not unless you were trading, i.e. buying and selling stuff for profit. Just selling your old stuff is fine. Gifts don't count as income. If the decision maker does decide that it's income (possible, because front-line staff don't always know the rules), ask for a "mandatory reconsideration" - those are important words to remember if JobCentre staff ever cock something up.
It would count as an occasional sale of personal belongings. Profits from this that are no greater than £1,000 a year aren't taxable and shouldn't count as income at all.
If you are selling your used stuff that you probably bought at some point for more money than you've now sold it for, then there is no profit. If for example you bought a games console new for £350 and somebody gave you £200 for it used. Turnover alone shouldn't count.
If they really want to be cunts, then they can ask you to prove when and for how much you bought things. But I would just go and tell them that you freed up some cash by flogging your used belongings. A lot of people do when they're skint.