If you order death certificates for events before 1969, actual dates of birth are not recorded. Information on certificates is informant driven, even today, and information recorded may be sightly incorrect but not deliberately supplied as such.
If you order an historic birth or death certificate from the General Register Office at Southport, use the reference number from the many sites such as freebmd, FindMyPast, Ancestry or familysearch. If you do not use the reference number but give a date of birth or date of death which may be incorrect you might not get the certificate as the staff there may consider this to be a mis-match.
Again, if you order a birth cert from the GRO without a reference you will be asked to supply a place of birth which you may not know.
The same applies if you try to order a certificate locally.
Ordering a death direct from Warrington will cost £10 plus postage either £3 1st class or £1.50 2nd class, you will also have to answer questions you may not have the answers to
https://registrars.warrington.gov.uk/rafts/CopyCertificates/Process/Certificate/CertificateOrderForm.aspxsuch as the actual pace of death
Most people here choose to use the General Register Office with reference numbers for certificates.
Hope this helps.