If you've been earning enough to be paying NI contributions whilst in work (at least £146 per week), DWP would permit you to claim Contribution-based JSA for 6 months, any savings you may have are irrelevant. Gizmonster is referring to Income-based JSA, which can be claimed only if one is disbarred from claiming the other type of JSA.
You need to ask your employer how it proposes to deal with the redundancies; when I have been involved in this, we have agreed with employees that it will be stated that the employer made them redundant: fact, without any elaboration about volunteers etc. As far as I know, this holds water with DWP. Unless the system has changed, on receipt of a new applicant who states his/her employment ended because of redundancy, DWP contacts the employer to seek confirmation that this is indeed the case and that is the end of the matter.
BTW if an employee resigns from a job (not redundancy or another form of dismissal) he/she is disbarred from claiming any type of JSA for 12 weeks, not 6, as you believe.