Container trains regularly exceed the standard W6a loading gauge, usually requiring W8 or W10 gauge clearance like you say, but they aren't classed as "exceptional load" trains as such.
I think this is probably because W8 and W10 are standardised gauges, so although container trains require RT3973CON paperwork (giving specific details of route restrictions) they don't run under "X load" conditions.
A slight oddity is FXA / FQA type wagons which I believe are technically slightly outside W10 when loaded with 9 foot 6 containers, but given "special gauge" status on these forms on certain routes.
On a train document for a container train, the driver would see warnings like this, and needs to have the relevant paperwork that gives details of speed restrictions, cleared routes, and things such as specific platforms that might not be cleared.
WARNING-HC-VEHICLE(S) ON TRAIN CONVEYING 8 FT 6 INCHES HIGH CONTAINERS,
RT3973CON REQUIRED.
WARNING-EH-VEHICLE ON TRAIN CONVEYING CONTAINERS OVER 8 FT 6 INCHES HIGH AND
UP TO 9 FT 6 INCHES HIGH, RT3973CON REQUIRED. SEE FREIGHT
OPERATIONS MANUAL. NOTE THESE CONTAINERS MUST ONLY BE LOADED ON
WAGONS SPECIALLY CONSTRUCTED FOR THIS PURPOSE.
=================
X load traffic is normally given "bespoke" RT3973EXL paperwork which will accommodate non-standard infringements of gauge. Typical uses at the moment would be:
>Certain types of cars on top deck of double-deck car wagons (e.g. Dagenham - Garston and Dagenham - Mossend)
>Network Rail Tilting wagons for Switch & Crossing pointwork, as mentioned above (both loaded and empty).
https://www.flickr.com/photos/newspectrum/13482241645/
>Railvac movements (I believe the equipment is mounted on something like a KFA intermodal flat and appears to overhang):
https://www.flickr.com/photos/sparrowhawk7/8735323530/
WARNING-XM-VEHICLE(S) ON TRAIN CONVEYING EXCEPTIONAL LOAD.
RT3973EXL REQUIRED. SEE FREIGHT OPERATIONS MANUAL SECTION 'E'.
=================
Schedules for container trains would go through the timetabling process with a specified gauge such as W10 already taken into account. The gauge would also have to be taken into account during the planning process for diversions. For this reason some routes have an alternate which is also cleared (such as sending container trains from Southampton via Laverstock when the route via Winchester is closed, or sending Felixstowe trains via London when the route via Ely is blocked). Occasionally W10 trains might end up diverted via W8 routes, requiring care to make sure they are loaded accordingly. RT3973 forms already exist for containers on the alternate routes and normal diversionary routes.
Car trains are planned as "X loads" and given schedules accordingly, with regular diversionary routes specified on the RT3973 forms.
Tilting wagons are distributed from Beeston via the infrastructure network. For many of these trains there are WTT paths already in the system as "X" loads for use as required by tilting wagons (and also the Railvacs).
For example 6O24 Hinksey - Eastleigh has an alternate schedule as 6X24 and the same applies for many other infrastructure trips.
Other "X load" movements can be more irregular, such as military vehicles being moved for exercises.
Generally such movements need to be planned well in advance specifically as "X load" movements. There are various provisions (probably detailed in the rule book somewhere) such as that signal boxes en-route need to be informed and have copies of the RT3973 paperwork. RT3973 forms will exist for regular movements but may need to be specially created for unusual moves.
It would not be normal to move "X load" traffic on an ad-hoc basis and a VSTP (very short term planning) request for X load traffic would not normally be accepted unless there was a good reason for it. If "X load" traffic is en-route and needs to be diverted it would cause problems unless paperwork already exists for the diversionary route...
I think this unusual bridge movement probably ran as an X load, although such movements are rare these days:
Newly constructed Bridge 27 moves to NYMR from Cleveland Bridge by Class 66 No. 66137 | Channel: nymrfootage
Edit: Another common use for "X load" headcodes is for loco-hauled movements of multiple units on routes where they aren't officially gauge-cleared (shown in the sectional appendix).