If you miss the last Stansted Express ...

[gottaluvem]

.... to Liverpool St (12.30am), and can't afford a taxi, what are the options for getting into central London?

I understand there are National Express coaches that run later than the trains, but do they need to be booked in advance?

You can just book the coach online using your phone to book the next available.
If you check their website now for an example, you should see a coach available within the hour.

Details are on the NE website:
Can I buy my ticket to Stansted Airport from the National Express coach driver?

Yes* you can, however services may be full with pre-booked customers, so it is always advisable to purchase your ticket in advance.

however services may be full with pre-booked customers, so it is always advisable to purchase your ticket in advance.

Thanks. This is the key bit of info I needed.
(Not ideal for flight delays).

There are at least 2 bus companies on that route so buses go about every 15mins between them. Never had any issues getting a ticket on board. Google the route for company details 👍