There are two types of Job Seeker's Allowance; the first is contributions based, which means that if you've paid enough into the system, you are entitled to claim JSA for up to six months based on that contribution. This means they do not evaluate your claim based on household income or savings.
After six months, you then move to means tested benefit, at which point any savings over, I think, about £16,000 (I could be way out on this, TBH, it's the figure I have in my head but not sure why), are then taken into consideration, as is any other household income, e.g. maternity pay from a spouse.
You can't do voluntary work and claim as other people have said, becase you're not elligible for work. However, there might be more to it than this. When I sign on the question is always phrased 'any voluntary work over 16 hours', so you may be able to do some voluntary work, but certainly not a full weeks worth. Same goes for training courses.
However, there is something called the rapid restart programme which is designed for people taking up voluntary work, training programmes or temporary positions, where you know they will end at a set date and saves having to jump through all the hoops again.
If you're not working and not doing voluntary work that would prevent you from claiming, then you really should sign on. Some friends of mine have been out of work since Feb and have been living off savings saying that the amount you get isn't worth the agro. That might be true (it's actually about £250 a month) but the key thing about signing on is that they also pay your NI contributions. You can also get help with travel costs to interviews. I've had about £150 of expenses paid so far – it's very expensive to travel into London during rush hour, about £30 return each time. so this really makes a difference.
Best of luck with finding work!