The final regular timetabled steam train operated from Preston to Liverpool on 3rd August 1968.
On 11th August 1968, a train known as the "Fifteen Guinea Special", due to the somewhat expensive tickets, ran from Liverpool Lime Street via Manchester Victoria to Carlisle and back. That's a reasonable distance.
Not saying that that the latter was the definitive last ever long distance steam service, but it might just be up there, especially since BR introduced a mainline steam ban the following day.
With one exception, until steam workings were allowed to resume in the early 1970s. the 15 Guinea Special on 11 August 1968 was the last steam passenger working on BR. The exception was Flying Scotsman, for which Alan Pegler had a contract with BR to allow steam passengers excursions for several years, and there were several steam hauled tours into at least 1969 or 1970. Those ceased when Scotsman made its ill-fated (financially) trip to America.
As for steam working regular, daily service trains, the last workings covering 100+ miles were the Southern Region Waterloo - Bournemouth / Wemouth services that finished in July 1967.
Other steam "pockets" had ceased in March 1967 (Shrewsbury to Chester / Birkenhead, and the few residual workings between Shrewsbury & Aberystwyth). Summer (mainly) steam workings such as Preston - Carlisle, Leeds - Carlisle & Leeds - Blackpool had mostly ceased during 1966.
Some Bradford to Leeds or Wakefield portions retained steam power until late 1967.
After that, there were shorter workings in the Preston area (to Manchester Victoria, Blackpool South & Liverpool Exchange ) during 1968, until that final working to Liverpool Exchange on 3 August 1968. There were also a few steam replacements for failed diesels during early 1968, including at least one from Preston to Crewe.
The only "longish" steam workings in late 1967, and in 1968 were railtours, which (apart from the 15 Guinea Special) continued until 6 "final" specials on 4 August 1968.