Hello tanker. There were meetings between the SR and LNER on a daily basis through goods wagons, whether in the common user pool or not. The wagons not in the common user pool would be loaded in the LNER or SR and sent to the customer in the SR or LNER for unloading. Under typical NER/LNER rules one consignee putting 2 Tons of traffic for one single customer at one site could be provided with one wagon with which to carry that traffic. Once emptied it was meant to be returned to the point of origin as quickly as practiable. This was supposed to prevent the "evil" of transhipment, which was the main reason for the abandonment of broad gauge. Of course, transhipment took place on a daily basis at hundreds of sites across all the main line railway companies because a significant fraction of general goods traffic was in consignments of less than 2 tons to one customer at one site or to be distributed to multiple sites of that customer. Peter Tatlow was motivated to research his books because as a child in WWII he wondered why his LMS locality seemed to have so many LNER wagons. Even the typical GWR country branch would not have been served exclusively by GWR wagons. Some of Tatlow's shots of former NER wagons are actually taken during the mid-1920s at Barmouth GWR!
Most carriages on a post-grouping railway are of that company, with a small fraction of through carriages or through trains from other companies, but wagons came from almost anywhere. FYI - the LMS was No.1 for cattle wagons with the GWR No.2 The LNER was No.3 and the SR No.4 but both the SR and LNER together did not outrank the GWR. Steve Banks says that race traffic is an underestimated traffic, with significant numbers of racehorses being moved about the country as well as racing excursions to places such as Doncaster, Cheletenham, Aintree and Ascot as well as lesser courses at Wetherby, Newcastle, Lincoln, Chester and York.