I'm afraid I can only offer a few minor bits and pieces: Timothy von Halle's middle names, per the electoral roll, are 'Walter Laurence'; also from that source Henry G. Buckmaster's middle name is 'Gerald'. Per Companies House records he was indeed b. 1955, and is a fund manager. Also per Companies House, Timothy von Halle (also b. 1955) is a banker, and in the nineties an executive with Merrill Lynch. Sarah L. Sassoon was b. 1957.
Timothy von Halle's parents were Walter F. E. von Halle (I imagine the Walter Franz E. von Halle b. 1907, d. 2004) and (m. 1951) Josephine M. L. Dunne. Walter seems to have married 2ndly, 1960, Diana M. H. Hutchinson. I can't find a U.K. birth record for him so, as his name might reasonably be thought to imply, he was presumably born elsewhere (most likely Germany).
EDIT: Naturalisation certificate on National Archives site gives 'Walter Franz Erich von Halle. From Germany. Resident in London', this dated 6 February 1951.
Armed with this second middle name (amazing the difference it makes in the search results one gets!),
thepeerage.com, citing BP 2003 vol. 1, p. 1164, shows that Walter's second wife was Diana Margaret Hely Hutchinson, dau. of Maurice Robert Hely Hutchinson, M.P. for Hastings (grandson of the 4th Earl of Donoughmore) and Melina Agnes Mary, dau. of Adm. Sir Colin Richard Keppel, an equerry to Kings Edward VII, George V, Edward VIII, and George VI. From there, as one might expect, is descent from the Earls of Albemarle (Sir Colin's grandfather the 4th Earl). Sir Colin's wife, Henrietta Mary, was daughter of Maj.-Gen. Richard Blundell-Hollinshead-Blundell, which family I thought were gentry (I definitely remember the distinctive name) but don't appear to be in Burke's Family Index. Possibly I misremember, as checking my files shows the name to appear in the Alston formerly of the Tofte pedigree, which might be where I saw it.
Walter's father was Dr Ernst Hermann von Halle, of Grünewald, Berlin.
Here's the URL for anyone interested in tracing further ancestry- I just wanted to give an outline!