In England and Wales you can apply for any birth and death certificate. However they say this on the website.
Q3. What information do I need to apply online?
To get the fastest response, you should provide the GRO index reference number for the certificate that you are interested in, but it isn’t essential. You will be prompted to supply further details for more recent births and deaths (within the last 50 years) as you complete the online application form. If you are unable to complete the mandatory fields, then you will not be able to apply online.
This was brought in a few years ago to make identity theft more difficult.
Ken