[6] The 2nd Baronet, Sir Christopher Conyers married Elizabeth Langhorne, heiress to an estate at Charlton, Kent.

Sir Baldwin Conyers, 4th Baronet died without a male heir and the Horden estate was sold.

The baronetcy passed to his cousin, Ralph Conyers of Chester le Street, who was a great-grandson of the first Baronet.

[13] Although on 10 May 1800, he had attended Westminster Abbey for the funeral of his Gibside heiress cousin, Mary Eleanor Bowes[14][15] – acknowledged as the wealthiest woman in England[16] – he accepted no aid from his relatives at Gibside, the coal-rich estate in the Derwent Valley, County Durham, that his ancestor, Sir William Blakiston had owned.

Robert Surtees wrote in February 1810 that although Sir Thomas Conyers had a number of "patrons" who helped him financially, it was only from his relative, "the late George Lumley-Saunderson, 5th Earl of Scarbrough", that the baronet experienced "kindness" during his final years of hardship.

Surtees was modestly successful in his appeal for funds and Sir Thomas, "now in his 72nd year", was moved to more comfortable accommodation in a private house on 1 March 1810.

Sir Bernard Burke, in his 1861 work "Vicissitudes of Families", presents a chapter entitled "The Fall of Conyers" which concludes with the following: "Magni stat nominis umbra!