In summer 1966 there was a 10.30 from Poole to York via the Great Central on a weekday (10.54 to Newcastle on Summer Saturdays). A Peak would be a bit unusual on a GC, so perhaps it was from a year or so later when a train ran via the Midland as I have read somewhere that it took a while to allocate all the new headcodes.
The Great Central closed in September 1966. The Poole-York and vice versa were daily trains that ran via the Great Central until closure, going via Banbury, Reading West Curve and Basingstoke. After the Great Central closed they were diverted to run via Birmingham. They didn't work on the LSWR main line north of Basingstoke.
There were also four Great Central summer Saturday services in each direction that had their last summer on the Great Central in 1964. These were the Sheffield-Portsmouth, Leeds-Bournemouth, Sheffield-Bournemouth and Bradford-Poole, the first 2 of these running southbound overnight.
In 1965 these were diverted off the Great Central, the Sheffield-Bournemouth to reach Oxford via Worcester, the others to reach Oxford via Market Harborough and Bletchley. Working timetables show the Market Harborough and Bletchley route also being used in 1966 but that didn't happen. Instead the trains ran up the Midland Main Line to Brent then via Kew to reach the LSWR main line north of Woking.
The 2 overnight trains worked through onto the Southern Region with Peaks with (I think) loco changes at Basingstoke. There are a few photos of the northbound return workings on the LSWR main line between Basingstoke and Woking.
It has the headcode 1E55 so it is not the same train, or possibly just not the same timetable period, as referred to by the OP
1E55 was the Portsmouth-Sheffield.
Inter-regional headcodes for trains terminating on each Region were:
E - Eastern
M - London Midland
N - North Eastern (not used after merger with Eastern)
O - Southern
S - Scotland
V - Western
The Eastern and North Eastern Regions merged in 1967, but the comprehensive changes to headcodes only happened in May 1969. Up to 1968 trains heading for old North Eastern region destinations still had N headcodes.
In the 1966 Working Timetables the Bournemouth-Leeds and Bournemouth-Bradford trains still used the 1N72 and 1N63 headcodes left over from their Great Central days. I don't have any working timetables that show whether those headcodes were retained in 1967 and 1968.