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Grimwade speculates that Burrage Davenport was 94 years old in 1843 when he signed an apprentice's form.
There were two men by that name.

Burrage Davenport I.
Born 1748.
Christening record for St Andrew, Holborn dated 16th March 1748, father William and mother Ann.
Married Sarah Bailey 1773.
Marriage record for St Ethelburgh, Bishopsgate dated 24th March 1773.
Died 1819.
Burial record for St Mary, Ealing dated 9th June 1819 aged 71 years. Last address Old Brentford.

Burrage Davenport II.
Born c1776.
1851 UK Census shows place of birth as St Leonard, Foster Lane. Christening record not found but the inference is that Burrage Davenport (I) who was recorded in Foster Lane in the Parliamentary Report 1773 was his father especially as he is known to have married in 1773.
On both 1841 & 1851Census he is shown as a merchant.
Died 1863.
Burial record for St John, Hampstead dated 11th February 1863 aged 86 years.

DAVENPORT, Burrage II

His application for freedom by patrimony in the Clothworkers Company in 1800-01 records he was born in 1778.
As a bachelor of the parish he married Hannah Kitchener of Russington, Sussex at St Mary le Bow in 1803.
Christening records in 1802 -11 at All Hallows Staining of children of Burrage and Hannah Davenport show him as an insurance broker of Fenchurch Street and in 1812-14 at St John, Hampstead as a merchant of Church Row, Hampstead.
The UK Census for 1841 and 1851 recorded Burrage and Hannah in Fulham.
His wife Hannah aged 76 years died there in 1857 and was buried at St John, Hampstead.
Letters of Administration for the personal estate of Burrage Davenport, gentleman and widower late of 2 Warwick Gardens, East Kensington, who died there on 4th February 1863, were granted to his daughter Sophia Frances (born in 1814). The value of the estate was under £300.