It looks as if Edward Frost was never baptised which makes tracing his parents difficult. We know from Edward Frost's marriage to Ellis Cowdery that his father was Thomas Frost and that Thomas' occupation was gardener. The 1851 Census shows Edward to be age 60 [=1790/1791], a shoemaker and born in Lewisham, Kent. The 1841 Census gives Edward an age 45 [=1791-1796] but has Y in the Whether Born in Same County column (i.e. Middlesex). The best bet appears to be 1791 at Lewisham.

While there are lots of marriages of Thomas Frost at about the right time none of these seem to be in Lewisham. The nearest appears to be in 1787 at Southwark but most of them are in the City or towards Hackney.

A number of Frost families could be related to Edward.

Connection to the France family

One of the witnesses to the marriage of Edward's daughter Sarah to John Evans was William France. William France married Jemima Bennett in 1801. Jemima France was a witness to the marriage of Charles Frost to Mary Ann Wright in 1828 and also to the marriage of Eliza Frost to Richard Adams in 1846 (but this could have been the daughter, Jemima, of William & Jemima). In both cases the other witness was Geo Yarrow. Eliza appears to have been the daughter of Thomas Frost, coach painter, and Judith.

To link these Frost families, I would expect Charles' father (unknown), Eliza's father (Thomas) and Edward to be brothers (or maybe cousins). However, Eliza's father was born in the Southend area of Essex and although Charles' wife came from Colchester in Essex I haven't been able to link them or link either of them to Edward.

The families may simply have known each other through attending St Leonard Shoreditch.

Lewisham

Edward was born at Lewisham according to the 1851 Census. There were (at least) 3 Frost families in the late 1700s in Lewisham where the father was Thomas but no Thomas was a gardener (which according to Edward's marriage entry in 1845 was his father's occupation - but he could, of course, have changed jobs) and none of them was raising their family in the early 1790s. Thomas & Sarah Frost had children baptised in nearby Bermondsey in 1785,1787 & 1788 but Thomas was a mariner and later a victualler, so not a gardener. Also a Thomas & Mary had a child baptised at Newington in 1785 and Thomas & Mary (possibly the same family) had children baptised in Lambeth in 1784 & 1791 - no occupation given.

Gardeners

Edward's father, Thomas, was recorded as a Gardener when Edward remarried in 1845. The only Thomas that I have found who was a gardener was at Farnham some 60 miles from Lewisham and his children were baptised from 1812 onwards.