Re using local offices
You can order certs from the office local to the event (some counties now centralise everything to provide a countywide service). Ordering & payment options vary, the best way to check is to use the registrars pages from the relevant county council website.
Northumberland as an example is split into regions with the main office based at County Hall, Morpeth.
Birth and death certificates are relatively easy, although you don't need the gro reference it's useful as a guide to when the event would have been registered.
Marriage certificates are somewhat different as each marriage veneue (eg church or chapel) use their own register. In any district there are a large number of venues and therefore a large number of registers, without knowing the venue it's very unlikely the registrars would be able to search through them to locate a particular marriage.
I've used many local offices over the years for birth and death certs plus the odd marriage cert where I've found a news report or perhaps a transcription of a register to identify where it took place. Most of the time they are quicker than the GRO but you have to do a bit of work yourself in advance. Price wise they usually match with the GRO though some may charge postage.
The main reasons I use them is that they have the original registers and whenever possible I ask for a copy of the original rather than a transcription. It removes the steps where errors can creep in with GRO certificates due to the multiple transcriptions used in process.......note though that not every office is able to oblige and may issue a handwritten or typed certificate based on the original register.
https://www.northumberland.gov.uk/Registration/Order-a-copy-certificate.aspx#orderacopycertificate