Some famous residents of St Nicholas-at-Wade include the following. The village connections of the Bridges family and TJ in particular were celebrated on 28 June 2003 in 'Bridges Between Nations', the Sixth John Briggs Memorial Lecture, at which Ben Jones (grandson of TJ) and Lord Bridges (grandson of Robert Bridges) both spoke, and international soprano Christine Hubbard sang some songs with words by Robert Bridges.
The Bridges family, ancestors of Sir Robert Bridges (Poet Laureate) etc. The current Lord Bridges GCMG is still titled The Second Baron Bridges, of Headley, Surrey, and St Nicholas-at-Wade, Kent. The Bridges Family was very influential in St Nicholas-at-Wade for over 200 years, living at St Nicholas Court (shown here in a painting by Rodney Tapp). Robert Bridges was born in 1844 and educated at Eton and Corpus Christi College, Oxford. After travelling extensively, he studied medicine in London and practised until 1882. He was Poet Laureate for 17 years from 1913-30. His only son Edward, 1st Baron Bridges of Headley, county Surrey and St Nicholas-at-Wade, county Kent, KG, PC, GCB, GCVO, MC was Secretary to the Cabinet 1938-46 covering World War II and the Nuremberg Criminal War Trials. On 7 April 1957 he made a radio appeal on behalf of the village church. Edward's brother was Lieutenant General Sir George Tom Molesworth Bridges KCB KCMG DSO — his ashes are in the churchyard. P.G. Wodehouse's sister-in-law also allegedly lived at St Nicholas Court at one time.
Although he does not seem to have been a resident at any time, it's interesting to note that on 13 June 1948, Dylan Thomas introduced the BBC radio programme "Country Magazine" live from the Bell Inn. There is a fascinating article about this broadcast (check out the linked local press coverage too).
Finally, judging purely on the basis of the "number of column inches in the world's press" (primarily USA), the most famous residents appear to have been dogs. Out of over 300 articles mentioning St Nicholas-at-Wade on newspapers.com, over 50 of them refer to a single incident in 1955 when "Woo Woo" (actually Bow-wow), the dog of "Mrs Triston Jones" (actually Tristan: son of TJ above), fell down a 40-foot unused sewer and was rescued four days later by Ross Baldock, whose own dog "Bella" had fallen into the same hole. The next most popular mention is Sofer Whitburn's greyhound "Wise Counsellor", who died of exhaustion (the hares' revenge?) during a coursing meet in 1930.