From a MCRUA newsletter:
FREIGHT ON THE MID-CHESHIRE LINE
The level of freight traffic on the line is only a shadow of its former self but members may be interested in a summary of what currently operates:
1. 11 limestone trains per week from Tunstead in the Peak District to Northwich (Lostock and Winnington) and the corresponding empty workings. Two return trains are scheduled to run each day apart from Tuesday, Thursday and Sunday, when only one train is scheduled to operate (although there are paths for two trains each way on Tuesdays and Thursdays if required). The trains run every day of the year except Christmas Day. The limestone is for the manufacture of soda ash and the traffic has used the line on a regular basis since 1874. Each of the present trains normally conveys 24 wagons, each of which weighs 102 tonnes when loaded making a trailing load of 2,448 tonnes. Motive power is a class 60 diesel locomotive, 100 of which were built by Brush for British Rail in the early 1990s. In steam days there were 8 return trips per day because each train only conveyed 16 wagons with a smaller carrying capacity plus a brake van. There was also a third works at Northwich (Wallerscote) until 1984.
2. On Tuesday and sometimes Thursday a return train operates between Warrington Arpley and Dowlow in the Peak District. This train conveys powdered limestone from Dowlow bound for Mossend (Scotland).
The wagons are attached to an Enterprise freight working to Mossend at Warrington. The Dowlow train also conveys tanks of locomotive fuel to and from Peak Forest and empty wagons to and from repair. Motive power for this train is currently an aged class 37 diesel locomotive from the 1960s.
3. Coal traffic uses the line on Mondays, Wednesdays and Fridays on its way from Scottish opencast sites to Earles Sidings near Hope on the Manchester-Sheffield line for the manufacture of cement. The empty train is often seen returning through Altrincham at around 07.00.
4. Compacted domestic refuse is taken by rail from Northenden Junction to Roxby near Scunthorpe. This traffic ran 5 days a week until recently but now often only operates on two or three days a week, presumably due to the increased recycling of refuse.
5. Freightliner operates a stone train between Dowlow and Garston (Merseyside) via the Hartford curve on an occasional basis.
6. Stone is occasionally conveyed by rail on a Wednesday evening from Dowlow to Northenden.
7. Trains between Runcorn and Warrington Arpley travel via Northwich Sidings to run round (reverse).
8. Freightliner Heavy Haul light engines between Crewe Basford Hall and Earles Sidings.
9. The West Thurrock/Walsall to Earles Sidings Lafarge Cement empties hauled by Freightliner is now also a regular user of the line. This train is routed via Crewe, Middlewich, Northwich, Altrincham, Northenden-Hazel Grove and Chinley.
Number 9 sounds like what you are describing. Number 8 would be another Middlewich line working.