Cheapest accommodation beginning to stoke anger at St Andrews? (8)

I believe the answer is:
steerage
'cheapest accommodation' is the definition.
(cheapest accommodation on a ship)
'anger at st andrews?' is the wordplay.
'anger' becomes 'rage' (rage is a kind of anger).
'at' means one lot of letters go next to another (I've seen this in other clues).
'andrews?' becomes 'ee' (I am not sure about this - if you are sure you should believe this answer much more).
'st'+'ee'='stee'
'rage' put after 'stee' is 'STEERAGE'.
'beginning to stoke' acts as a link.
This may not be right. Some or all of it may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for steerage that I've seen before include "Cheapest part of liner" , "Formerly cheapest space on board" , "Densely-packed travellers here" , "cheap way to travel" , "government" .)
