Manningtree-Harwich Town services run entirely within the Tendring District Council area.
Also in Tendring, there’s a handful of Kirby Cross- Walton shuttles at start and end of service (and all day Sunday). There’s a similar set-up on the Witham-Braintree branch, entirely within Braintree District Council.
And rounding off Essex, Colchester - Colchester Town shuttles are obviously entirely within Colchester Borough Council.
More obscurely, the 06:50 Fishguard Harbour - Clarbeston Road (and 07:20 return) runs entirely within Pembrokeshire.
Scraping the barrel a bit, but in addition to the Cornish branches, there’s an 05:20 Penzance-Truro service entirely in Cornwall (presumably a unit for the Falmouth service).