a few thoughts -
I'd agree with
equationgirl - resigning is probably not a good option. you may well fall in to the 'voluntarily unemployed' situation and be disqualified from job seekers allowance - i'm not quite sure how you'd stand claiming ESA (benefit if you're too sick / disabled to work) but it gets more difficult to claim at fairly frequent intervals.
it may seem an easy way out of some of the hassle in the short term, but i can't help thinking it would probably cause more problems in the not too distant future.
there's no right to ask for redundancy. in some cases like this, an employer may think it's an easy way out of a situation (i managed to get a redundancy deal a few years back when i was in fairly crappy health, and it suited all concerned)
but employers may invoke a 'capability' process - in other words if they decide someone is no longer capable, through poor health, of doing their job, it can be legal to sack someone for being ill. although they do have to handle this carefully and with a proper process.
Gromit has mentioned 'constructive dismissal' - this may be a possibility, but (in most cases) you need to have 2 years' service or more with your employer, you usually have to show that you've at least tried to resolve things through the employer's grievance procedure before resigning, and there are now fees to bring a case to an employment tribunal. if you're even thinking of going down this road, you'll need some advice.
are you in a union at work? they ought to be able to offer some advice.
failing that,
ACAS do have an advice line that any employee can ring - you don't have to give your name and so on.
as for the specific hassle about when you take your certificate in - i'd be inclined to post it in (take a photocopy first and maybe sent it 'recorded delivery' if they are likely to be dificult
hope things get better for you soon.
as an afterthought - i've found
this page on action on depression website which seems fairly good, although be aware they are a scottish organisation, some bits of law may be different from england, and some of the links are scottish organisations.
time to change may also be worth a look.