No second marriage is to be found.

His death registration:

Surname First name(s) Age District Vol Page
Deaths Dec 1873   (>99%)
Hyndman John Beckles 60 Uxbridge 3a 14
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He could not be found in any of the 1841 to 1871 censuses.
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According to an internet report on slave ownership he was the son of a ‘wealthy slave-owner’ in this report on his mother:

Elizabeth Christian Hyndman (née Beckles)
Profile & Legacies Summary
???? - 1834
CLAIMANT OR BENEFICIARY
<span class="label label-silver">Non-Claimant Labels Here?</span>

Biography
Daughter of John Alleyne and sister of John Alleyne Beckles (both q.v.) of Barbados, Elizabeth Christian Beckles married Robert Augustus Hyndman, a wealthy slave-owner who died in Demerara and with whom she had two children, John Beckles Hyndman and Catherine Elizabeth Hyndman (each of whom also q.v.). In a statement from John Beckles Hyndman dated 21/11/1835, he affirmed that on 09/09/1834 Elizabeth Christian Hyndman died, leaving a will but no executors; the estate was left to her children John Beckles Hyndeman and Catherine Elizabeth Hyndman. Catherine Elizabeth Hyndman died on 16/06/1835 and John Beckles Hyndeman got letters of administration.
1 Baptism of an Elizabeth Christian Beckles, to John and Elizabeth, Marylebone, 04/11/1776. However, genealogical sources show Elizabeth Christian Beckles who married Robert Augustus Hyndman as born 21/02/1781 and baptised in Barbados. Consistent with this second source, the burial record for Elizabeth Christian Hyndman gives her age at death as 53 in 1834. It is possible that the earlier baptism was of a child who died.
2 Administration of the will of Elizabeth Christian Hyndman was granted 24/07/1835. In the will, she left her estate to be equally divided between her two children after numerous monetary legacies, the most material being provision of £300 p.a. for her 'dear adopted son Charles R. Hyndman' until he could provide for his family, and £800 p.a. to his widow and £50 to each of his children (£200 p.a. from the age of 8 if there were only boys but £100 p.a. each to boy and £50 each if girls if there were more children) if he died before he could make provision for them.
Sources
T71/895 Barbados claim no. 3. T71/1256: statement, dated 21/11/1835.
1 Ancestry.com, London, England, Baptisms, Marriages and Burials, 1538-1812, London, England, Deaths & Burials, 1813-1980 [databases online]; Brandow, Genealogies of Barbados Families p. 155.
2 PROB 111849/279.
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His report from the same source is:

John Beckles Hyndman
Profile & Legacies Summary
1813 - 25th Nov 1873

CLAIMANT OR BENEFICIARY
Biography

Son of Robert Augustus Hyndman (d. 1814) and Elizabeth Christian Beckles (d. 1834), and father of H. M. Hyndman, the British Marxist, and brother of Catherine Elizabeth Hyndman (q.v.). The ODNB entry for his son H. M. Hyndman describes John Beckles Hyndman as 'a West India merchant and benefactor of east London churches.'

Married Caroline Seyliard Mayers (daughter of Henry Adams Mayers of Barbados) at Cheltenham 01/01/1839.

Administration of the effects of John Beckles Hyndman late of Moorcroft House Hillingdon who died 25/11/1873 at Moorcroft House granted 21/02/1874 to Henry Mayers Hyndman the son and one of the next of kin, effects under £16000, resworn Nov 1876 under £18000; Administration of the effects of Caroline Seyliard Hyndman who died at 7 Hyde Park Square on 05/12/1848 granted to Henry Mayers Hyndman as administrator of John Beckles Hyndman 12/10/1874 effects under £3000.

There appears to be a family connection to the Hyndmans in Antigua claims: Robert Augustus Hyndman (d. 1814) appears to have been the cousin of Robert Hyndman, the father of John [Elliott] Hyndman and Robert Augustus Hyndman (1807-96), but this has not been substantiated and the source has no references. John Beckles Hyndman himself was the residuary legatee of Hugh Hyndman (q.v.).

Sources

T71/885 British Guiana claim nos. 626 (Plant. Houstown) and 627 (Rome); Chushichi Tsuzuki, ‘Hyndman, Henry Mayers (1842–1921)’, Oxford Dictionary of National Biography, Oxford University Press, 2004; online edn, May 2006 [http://www.oxforddnb.com/view/article/34088, accessed 8 Dec 2014].

H.M. Hyndman, The record of an adventurous life (London, Macmillan, 1911).

FreeUKGen, England and Wales Free BMD Database, Marriages, 1837-1983 [database online]; Ancestry.com, England, Andrews Newspaper Index Cards 1790-1976 [database online]. Children's names other than Henry Mayers taken from Ancestry.com, London, England, Births and Baptisms, 1813-1906 [database online], apart from Hugh Reginald and Caroline Seyliard (inferred from marriage announcements identifying John Beckles Hyndman as the father, England, Andrews Newspaper Index Cards 1790-1976).

National Probate Calendar 1874.

http://genforum.genealogy.com/hyndman/messages/331.html [accessed 09/08/2012].
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Cambridge Alumni has for him:

Hyndman, John Beckles.
Adm. pens. (age 20) at TRINITY, July 4, 1830. [Only] s. of Robert [Augustus,
of Demerara]. B. Mar. 18, 1812, in London. School, Eton. Matric. Michs. 1831;
B.A. 1835; M.A. 1838. Adm. at Lincoln's Inn, Jan. 15, 1833. A West India
merchant. Of Hyde Park Square, London, W., in 1864. Father of Henry M. (1861).
(Eton Sch. Lists; Inns of Court.)
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Their marriage registration:

Surname First name(s) District Vol Page
Marriages Mar 1839   (>99%)
HYNDMAN John Beckles Cheltenham 11 203
MAYERS Caroline Seyliand Cheltenham 11 203
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