He would undoubtedly been a member of the union - NUR or ASLEF. They were both subsumed into the RMT.
The RMT has excellent records, and I think that could be your first port of call.
http://www.rmt.org.uk/
meles
Meles: Definitely NOT. ASLEF remains independent to this day, founded 1880 and still going strong, my late father, and most other ASLEF members would have apoplexy at the thought of being subsumed into the RMT, ASLEF HQ Arkwright Road, Hampstead, London.
Back to the topic, the LNWR was subsumed into the LMSR when the grouping of mainline railways came into effect in Jan 1923, many of their records are held in the National Archives at Kew. A driver would almost certainly be a member of ASLEF, specially if he started in the footplate grade as a fireman or cleaner. Most of the very few footplate staff in the NUR had joined the railway in another grade eg, lad messenger before transferring.