Evacuating in a disused station

Never had to do that. There being no closed stations on the Central, bar British Museum, but you cant access the street from the old platform tunnels. Had to drop off some techni-guys at Old Ford Fanshaft ages ago, they were investigating water seepage!

Citysig is correct. The Line Controller would seek advice from staff on the ground, preferably an operating official, and then seek authority from the DOM before authorising a detrainment of this type.
This is obviously dependant on location and severity of the incident that is occuring. In a fire/smoke situation things would develop quickly and would require rapid decisions that took into account the risk levels of going or staying. In a defective train scenario where a more measured approach could be applied it would be more prudent to try other methods before going for detrainment, in this situation you could also deploy your staff in order to assist. As for location, Kings X disused for example is not an official detrainment point but was used on July 7th following proper operational considerations and deployment of personnel. Where as somewhere like the Old Ford Fan Shaft, which is specifically designed for an emergency detrainment, is a different prospect.
It is generally the case that detrainment would commence before the arrival of a Duty Manager (Trains), as they are normally remote from the incident and/or enroute. As a DMT, the first thing you do when you arrive on site is find the most senior member of LU staff and get an update, whilst ensuring that the correct protection arrangements are being followed (this is vital). You would then take the role of Silver Control and liaise with the appropriate level in the attending emergency services and the relevant LU staff in the incident structure. At this point you would also take control of traction current arrangements.

On the District, we have a disused station at St. Mary's (between Aldgate East and Whitechapel) but I wouldn't have the first clue how to evacuate there - I don't even know if there's any access to the surface anymore.

There is a general instruction that closed stations (including those just closed on Sundays) are to be considered part of the running line, i.e. they don't exist to all intents and purposes.

The platforms have a solid brick wall with cables on them. Also, AFAIK street access is no longer available - so it'd be a little difficult ;D ;D

The other disused station on the District, Mark Lane, only has a platform eastbound. Though it's not bricked off, there are plenty of cables in the way here too - and street access is extremely limited.

What are ,or were, the Authorised detrainment locations between operational Stations ?

There are emergency exit/entrance points at the fan shafts on the JLE.

it was just purely guesswork, trying to marry up my knowledge of both lhr and lul, might be wrong!

Having done road training on the Picc just before the T4 loop was opened (was it REALLY that long ago? ) we were told that indeed you would come into a locked compound where you would be met by BAA staff in order to complete any evacuation.