Not sure of an online list, but I've given it a go myself. Fleets listed geographically and chronologically for clarity:
British Rail
- Provincial "EXPRESS" (White/Black/Blue) (158701 - 872)*
- West Yorkshire PTE (Red/White) (158901 - 910)
*Units 158701-814 carried
EXPRESS branding in a gap in the blue lining bands, whereas units 158815-872 carried "Regional Railways" insignia following the rebranding of the Provincial sector during 1991. Scottish units quickly had "
EXPRESS" branding superseded by "Scotrail" insignia in place of "Regional Railways" in the early nineties.
Scotland
- National Express Scotrail "Swoosh" (White/Purple/Green/Orange) (158701 -736/738-741)
- First Scotrail (Blue/Pink/White) (158701-736/738-741)
- First group blue (158782/786/789)
- Scotrail Saltire (Blue/White) (158701-736/738-741, 782/786/789, 867-871)
Northern England
- Northern Spirit Transpennine Express (Plum/Gold) (158737, 742-744, 760-779/781, 158798-814)
- North West Trains (Blue/Gold) (158752-759)
- Northern Spirit WYPTE (Red/Grey) (158909)
- Arriva Trains Northern WYPTE (Red/Silver) (158901-910)
- Northern Rail (Blue/Purple) (158752-759, 784/787, 790-797, 815-817, 842-845, 848-851, 853, 855, 859-861, 872, 901-910)
- Tour de Yorkshire (Yellow/Black) (158849)
- Arriva Northern Refurbished (Blue/White) (Ultimately same as Northern Rail fleet list, plus 158782/786/789, 867-871)
Central England
- Central Trains (Green/Blue) (158780/782-797, 844-860)
- East Midlands Trains (White/Red/Orange) (158770/773/774/777/780/783/785/788/799/806/810/812/813/846/847/852/854, 856-858, 862-866)
Wales
- Wales & West Alphaline prototype (Silver/Blue/Orange) (158867)
- Wales & West Alphaline (Silver/Yellow/Blue) (158745/746)
- Wales & Borders (Silver/Blue) (158817-843)
- Western Mail (Silver/Grey/Red) (158842)
- Arriva Trains Wales (Turquoise/Cream)
- Arriva Trains Wales 'Executive' (Turquoise/Blue) (158818-841)
- Transport for Wales (Grey/Red) (Ultimately 158818-841)
West of England
- Wessex Trains (Silver/Maroon) (158745-749/751, 815/816, 855/856, 859-872)
- Ginsters Pasties (Black) (158819/821/827/841)
- First Great Western "Local Lines" (158745-751, 760-769, 771/776/778/798)
- Great Western Railway (Dark green) (Ultimately same as FGW "Local Lines" fleet listed above)
- Gunwharf Quay (Light blue promotional) (158798)
- Springboard (Light blue promotional) (158798)
South West
- South West Trains (White/Red/Orange) (158786/789, 880-889**)
- South Western Railway (Dark/Light Grey) (Ultimately 158880-889**)
**158880-889 were converted from 158737/742/743/744/772/775/779/781/802/808/814 respectively.
There might be some minor discrepancies in individual units on the fringes of the number ranges that wore Central Trains/Wessex Trains/Wales & Borders livery in the 1588xx series: These fleets were outside my area of expertise and there seemed to be some chopping and changing amongst them. More than happy to accept corrections.
I'm also unsure how many units received standard Arriva Trains Wales livery before the refurbishments commenced: I seem to recall a number of grubby Wales & Borders silver units going directly into the ATW 'Executive' scheme.
I've also omitted livery variations such as:
- "Central Trains" or "Alphaline" insignia on Provincial Express livery.
- South West Trains livery variations
- First Transpennine Express dark blue vinyls applied to lower bodysides of all Transpennine Express units and Regional Railways liveried 158750.
- Central Trains white "C" logos applied to cab ends of ex-TPE units.
- Northern Rail route pictorial vinyls