Given a lack of evidence for Jeremy P. Nunn at that place, it seems to me that Jeremy Nunn, of Kimpton, might be Joshua Jeremy Nunn (1955-), an investment manager who per companies house is of Lane House, Kimpton, and The Thatched Office, Manor Farm, Kimpton, Andover, Hants. Jeremy P. Nunn and Gylda J. Nunn at Bury St Edmunds, Suffolk per 2002 electoral roll, he a director recorded there 2003-7, 2014-15 with Tobias E. Nunn. Sources from 2021 show a Gylda Nunn working in healthcare in West Suffolk. Per companies house, the Jeremy P. Nunn of Bury St Edmunds is seemingly Jeremy Peter Nunn (1959-), of the village of Risby, near Bury St Edmunds, an agricultural engineer, formerly automobile sales contract director and sales service director for a golf course.
No evident birth of Jack A. J. Nunn, but a Joshua Alistair J[ack?] Nunn b. 1988 at Lambeth, mother Waterhouse; this fits with the 1985 marriage at Windsor of Joshua J. Nunn and Georgina F. Waterhouse. Per
192.com, Joshua Jeremy Nunn a company director at Andover, Hants., alongside Georgina F. Nunn.
The above would explain the lack of birth record for Jack Nunn, the first name of Jack Nunn's son, and the lack of evidence for Jeremy P. Nunn at Kimpton/ the records of Joshua Jeremy Nunn there.
Joshua J. Nunn b. 1955 at Trowbridge, Wilts., mother Sheil; 1952 marriage of Joshua A. J. Nunn and Helen M. Sheil matches details at
thepeerage.com (citing Telegraph notices) of marriage of Maj. (Joshua) Anthony James Nunn (-2013) and Helen Marjorie (-2004), dau. of Brig. William Anthony Sheil (1899-1945), of the Royal Artillery, C.B.E., D.S.O.; their elder son is given as Joshua Jeremy Nunn. Per BMD records Maj. Anthony Nunn b. 1927, buried at Pendomer, Somerset; he of the 10th (Prince of Wales's Own) Royal Hussars, in 1979 appointed to H.M. Body Guard of the Honourable Corps of Gentlemen at Arms. Per an Ancestry user-generated source, he b. Wexford, Ireland [there being no U.K. birth record evident] s. of Richard Narcissus Nunn (1896-) and Honor Louisa (1899-1976), dau. of - Delamain. R. N. Nunn doubtless the Brig. Richard Narcissus Nunn (1896-1970), of Alma House, Ferrycarrig, Wexford, King's Own Royal Regiment (Lancaster), who served in India (see
https://www.independent.ie/life/home-garden/homes/inside-the-25m-wexford-mansion-that-was-home-to-generations-of-the-nunn-family-40972650.html). His elder brother, Joshua Nunn (b. 1889), lived at Alma House until their father [evidently Joshua Loftus Nunn b. 1850] died in 1928, he then moving to Castlebridge House; they were of a family in business with the Guinnesses, supplying malted barley to the brewery in St James's Street. No doubt further research would be profitable. Presumably these are the Nunns in BIFR 1976, but I haven't access to my copy at present to check.