MummyOFone, I am not an employment expert, but I will give my 2p worth, if only to bump this up.
I don't know whether parental leave is a statutory right and if so, the conditions that come with it (perhaps an employment expert can help).
In my company, parental leave is a contractual right of every employee who has worked for more than a year. It is a total of 13 weeks (unpaid) for each child under 5 years and must be taken in blocks of 1 week, subject to a max of 4 weeks a year. It is subject to prior approval, so not an automatic right that it will be granted. Perhaps you could check your terms of employment for the specific details in your case.
Uwila, the leave you are referring to is called family and domestic leave in my company's case. I get 5 days of emergency unpaid leave a year eg to deal with childcare/family emergcencies. This is not subject to prior approval.
MummyOFone, unless the terms of your employment specifically allow, I don't think the company is legally obliged to to give you one year' off. But see if you can apply for sabbatical leave under the terms of your employment (again, if available, could be subject to approval and other conditions).
Alternatively, you could make an application under the flexible working regulations - bear in mind, no teeth - to make your return more manageable. Your company is under a legal obligation not to sexually discriminate against you just because you now have a child, so they do have to tread carefully as well, in considering your application for parental leave, sabbatical, flexible working etc - again, employment experts, help!
I would put resignation as the last resort. Don't solve the company's problem for them by doing so. Push to get approval for unpaid leave, whether under the terms of your contract or outside, in a specially negotiated bargain. Who knows, the company might pay you off or you might be made redundant - dunno if that is a good thing for you, but at least, you don't give up your rights.