British Independent Airlines 1946-1976 is a good source. It says the first Channel Trident 1E-140 was delivered to Southend in late May 1968 and the first commercial flight took place on 1 June 1968 (although it does not say where from).
"On February 16 1969, the Trident G-AVYE became the largest jet ever to land at Lulsgate Airport, Bristol, followed in May by the introduction of a Saturday afternoon inclusive tour Trident service from Lulsgate to Gerona on behalf of Mediterranean Holidays."
"By early 1968, Channel Airways was experiencing operating problems with its 1-11s from Southend, due to the runway length, and to local noise complaints, and so the airline moved most of its jet inclusive tour operations to Stansted."
"During 1968, Channel's inclusive tour flights from Stansted were operated by the 1-11s and Tridents, and the destinations served were Athens, Barcelona, Djerba, Faro, Gerona, Ibiza, Jerez, Lisbon, Las Palmas, Mahon, Malaga, Malta, Naples, Palma, Pula, Rimini, Rome, Split, Titograd, Tunis and Venice"
"Throughout 1969, in addition to its inclusive tour flights from Southend and Stansted, Channel Airways also flew jet inclusive tours from Edinburgh and Teesside to Alicante, Gerona, Ibiza, Palma and Venice."
The book goes on to describe the sagas of 1971 and the eventual collapse of Channel Airways after sending one Trident to Berlin and robbing spare engines off the other (sitting at Stansted) due to lack of cash to buy spares and the eventual sale of the aircraft to BEA.
It's not completely definitive, but if the 1-11s were struggling at Southend then I'd have to presume that commercial operations of the Trident at Southend were impractical and improbable.
Of course, Southend did see some later Trident "operations" (one way) as the final arrival for some of the BA Trident Twos in 1984 and 1985 - G-AZXM was one of the aircraft to have an encounter with a JCB there.