Citizens Advice outlines the different methods and notes that, when you're unsure of the dates, you have the option of sending the request on paper via the post (emphasis mine).
You can get a copy of a birth certificate by post from the General Register Office.
You should provide as much information about the birth as possible. If you do not know your exact date of birth, a search will be made for one year either side of the year you give. If an entry cannot be traced, you will get a refund.
You can download an application from the GOV.UK website at www.gov.uk or by emailing the General Register Office. You can pay the fee by credit or debit card or by a cheque payable to IPS. The contact details are:
General Register Office
Certificate Services Section
PO Box 2
Tel: 0300 123 1837 (Mon-Fri 8am-8pm; Sat 9am-4pm)
For details of fees for copies of birth certificates, go to the GOV UK website at www.gov.uk.