Just found my copy of another book on The Wisbech & Upwell Tramway, namely the Wild Swan Publications one, from 1982.
Amongst much interesting material there is a picture of essentially the 'only' signal outside the Wisbech East station limits. This was where the parallel Upwell single line diverged from the 'main' line to Kings Lynn near Wisbech Harbour Junction. As noted above the line was 'controlled' by telephone.
Although the passenger service was worked on an essentially out-and-back basis, with a round trip taking just under two hours it is worth noting that at busy 'harvest' times the freight service could be quite intense. An extract from a 1949 Summer timetable (in the freight-only era) shows a morning round trip, then two trains in succession down to Upwell, one of which returned fairly soon, leaving the second to load. Once the first train had got back to Wisbech there were then three trains in succession down to Upwell, two of which were to be double headed. This provided no fewer than six locomotives and crews down at Upwell simultaneously. (There were six roads at Upwell, together with a central additional run-round release between a couple of them. The six trains would then return at 3.15, 3.20, 3.30, 4.14, 4.45 and 4.50p.m.! Arrival at Wisbech East was timed to connect for various produce trains for destinations as far away as Scotland and London. However, 'passing' in mid route appears to have been very much an exception.
Possibly worth clarifying that the Rev W Awdry hardly needed to 'visit' the Wisbech & Upwell because he was the local vicar of Emneth, which parish included part of the line. Another famous 'railway reverend', the Rev Edward ('Teddy') A Boston, later of Cadeby, was a curate at Wisbech.
The book also talks very clearly about the Great Eastern pedigree of the line with no suggestion that it was a separate company, albeit constructed and operated under rather atypical legislation for a 'main line' railway.
From the Directory of the Railway Companies of Great Britain by Donald J Grant, the Wisbech and Upwell Tramway is listed separately and the entry notes that there was an earlier attempt to build an 'independent' line. However, "The GER built, owned and worked the line".