DPB online records that Sir David died in 2021. A probate search reveals he died on 13 May 2021 (probate granted 13 Jan 2022). He was not on the Official Roll of the Baronetage.
The 14th baronet (Broughton of Broughton, E 1661) is (subject to entry on the Roll) the 13th Baronet's half-brother Geoffrey Delves BROUGHTON b 1962 m 1986 Karen Louise WRIGHT and has issue: Kathryn Louise Delves b 1988, Jennifer Anne Delves b 1989 (m 2015 Anthony Andrew FATA and has issue a dau), Peter Thomas Delves, hp b 1991 and Christopher James Delves b 1997. The new Baronet lives in Canada