What are “independently timetabled networks” are we referring to individual lines that do not interact with others, or collective services of an operator? Anything that is timetabled with ANY consideration for connections onto other services does not count.
While there's a small amount of interaction at South Parkway-Hunts X and Chester, Merseyrail is as close to standalone as you're going to get.
As well as physically crossing the paths of other services at those locations, Merseyrail is supposed to be timed to connect with Northern services at Southport, Ormskirk and Headbolt Lane, so the the timetable is the combination of those 2 constraints, but depot moves do not leave “the Merseyrail network” while they remain on Network Rail infrastructure.
Chester is closer, with almost exclusive use of platform 7. To be independent, you definitely have to have your own platform.
During engineering works, Wigan Wallgate - Headbolt Lane shuttles have run, not timed to connect with anything and with the constraint being the need for the unit to complete a return trip within an hour. It didn’t visit a depot either.
In a similar way, the St Erth to St Ives, Liskeard to Looe, Sudbury to Mark's Tey, Romford to Upminster, and Grove Park to Bromley North branches are all run as independent entities, from their own bay platforms off the main line.
Though one advantage of the integrated GWR is that they do timetable things (as far as possible) to connect nicely and they do hold connections
GWR branches etc, despite bay platforms, can not count if timetabled to connect with main line services, even if connections aren’t held.
The Romford - Upminster or soon to be Liberty Line may actually be the most hyper efficient operation on the network, with a modern electric unit on its shuttle and no need to be timetabled to connect with anything more because of the frequencies on the main lines at each end and its proximity to Ilford depot has always meant the ECS mileage is absolutely minimal. This may be the best heavy rail example.
C2C is probably the closest you'll get to "self contained" network on the mainland.
Tons of freight. Barking Riverside / LO. Services to Liverpool Street.
On days when it doesn’t touch Stratford, the entire LT&S passenger timetable from Fenchurch Street is completely isolated from the rest of the network.
Unless the passenger timings are massively compromised by any through freight, then this doesn’t rule it out at all.
If we’re talking about a route that is segregated, has no through freight or passenger services from other routes, no on/off empty stock moves and also does not get affected by service disruption I.e. being held for connections, then I suspect the Stourbridge Town branch is the only example.
The ENTIRE “Stourbridge Shuttle Network” definitely works. Timings are nothing to do with the Snow Hill lines and it doesn’t need any depot movements. There should be some competition between it and the “Liberty Line Network”