Anyone, including overseas residents, can order certificates online and pay securely by credit card, as described at https://www.gro.gov.uk/gro/content/certificates/default.asp.

Fees are listed at http://www.gro.gov.uk/gro/content/certificates/fees.asp - £9.25 for full birth, marriage and death certificates. Note that some commercial sites charge MUCH more.

The full GRO reference can be obtained from copies of the GRO indexes which are held by many libraries and record offices, or possibly from FreeBMD and some other sites.

FAQ8 (Frequently Asked Questions) says
If you do not have the GRO index reference you may still apply online for any event which took place on or after 1st July 1837 to 6 months from the current date (for marriages this period is extended to 18 months). A 3 year search for the index reference will be carried out. You must supply the exact date of event if you have it. If you don't have the exact date enter 01/01/YEAR and we will search the specified year and one year either side.