Ah-ha! Got it working.
These were the errors that clued me in:
[3492] main input debug: Creating an input for '
http://webdev/aenetworks/assets/shop/vi ... nal_031014 720.mov'
[3492] main input debug: using timeshift granularity of 50 MiB, in path 'C:\Users\gareth\AppData\Local\Temp'
[3492] main input debug: `
http://webdev/aenetworks/assets/shop/vi ... nal_031014 720.mov' gives access `http' demux `' path `webdev/aenetworks/assets/shop/videos/History_Spring_Sizzle_45_Final_031014 720.mov'
[3492] main input debug: creating demux: access='http' demux='' location='webdev/aenetworks/assets/shop/videos/History_Spring_Sizzle_45_Final_031014 720.mov' file='\\webdev\aenetworks\assets\shop\videos\History_Spring_Sizzle_45_Final_031014 720.mov'
[3492] main demux debug: looking for access_demux module matching "http": 12 candidates
[3492] main demux debug: no access_demux modules matched
[3492] main input debug: creating access 'http' location='webdev/aenetworks/assets/shop/videos/History_Spring_Sizzle_45_Final_031014 720.mov', path='\\webdev\aenetworks\assets\shop\videos\History_Spring_Sizzle_45_Final_031014 720.mov'
[3492] main access debug: looking for access module matching "http": 20 candidates
[3492] access_http access debug: querying proxy for
http://webdev/aenetworks/assets/shop/vi ... nal_031014 720.mov
[3492] access_http access debug: no proxy
[3492] access_http access debug: http: server='webdev' port=80 file='/aenetworks/assets/shop/videos/History_Spring_Sizzle_45_Final_031014+720.mov'
[3492] main access debug: net: connecting to webdev port 80
[3492] main access debug: connection succeeded (socket = 1172)
[3492] access_http access debug: protocol 'HTTP' answer code 404
[3492] access_http access error: error: HTTP/1.1 404 Not Found
Effectively, I had a space in my MRL which for some reason the VLC plugin didn't seem able to handle. All sorted now, though. Thanks.