The GWR had running rights to Manchester London Road, and I seem to recall these operated as GWR services throughout
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Also Birkenhead (the northern outpost of GWR metals) to Penzance is a possibility. From a distance point-of-view, in those days any services like that would almost certainly have run via Shrewsbury, Hereford and the Severn Tunnel.
The GWR rights were to Manchester Exchange, not London Road, from the joint LMS/GW line from Chester to Warrington, which had running powers over the LMS via Earlestown on to Manchester. In practice I believe the GWR did not provide any locomotives for passenger services through to Manchester, which were wholly LMS, but did operate freight services, it being an advantage to have their own freight terminal in the city.
I believe there were Birkenhead-Penzance through carriages at times, although these were well trumped by the Glasgow-Penzance through coaches which shared the same route (and possibly the same trains) south of Shrewsbury. There was passenger accommodation, but also extensive van provision, as the principal user of the through operation was mails. The GWR outpost at Birkenhead Woodside of course looked across by ferry to Liverpool for much of its business.
The through Glasgow coaches were still running in the 1960s as I recall the morning 1000 from Taunton to Liverpool, via Hereford, which had come through from Plymouth, had the two coaches at the front through to Glasgow, which were detached by the diesel at Crewe when the main Liverpool train changed to an electric loco, and then added to the afternoon Euston to Glasgow service which came through Crewe at that time. They were popular with sailors travelling between Devonport and Rosyth.
