Hello Philip
Your line I'm fairly certain also goes back to Philip Larcher of La Mothe, Poitou
These are the children I can find for Andrew Larcher and Rebbeca Judith:
Ann Rebecca Larcher born 28 Nov 1801 baptised 1 Dec 1802 St Matthews Bethnal Green
Esther Larcher Baptised 2 Sep 1804 St Leonard Shoreditch Adress: Worship Street
Mary Ann Larcher Baptised 4 May 1806 St Leonard Shoreditch Adress: Worship Street
Elisabeth Larcher Baptised 4 May 1808 St Leonard Shoreditch Adress: Worship Street
Harriett Larcher Baptised 23 Jul 1811 St Leonard Shoreditch, Adress: Worship Street
Andrew Larcher Baptised 13 May 1813 St Leonard Shoreditch, Adress: Worship Street
Thomas Mark Larcher baptised Non-conformist chapel, born 15 Jan 1820 No 1 Gibraltar Gardens, Bethnal Green
The last is the significant one, because, Andrew Larcher the father is still living there, Gibraltar Gardens, on the 1841 Census, seemingly widowed, aged 65, working as a Silk Weaver.
This, through the age, allows him to be identified as the son of John Larcher and his wife Ann, born at New Inn Yard, Shoreditch and baptised 15 Nov 1777.
John and Ann were having children 1764-80, so John's likely birth year would be around 1738-42.
I am therefore sure he is also a son of Andrew Larcher I and Ann Field, as we know they had one son Philip Larcher, baptised at the Anglican Church in Wandsworth, 1735, then a daughter Catherine Larcher in Shoreditch 1744 (NEW INN YARD also their adress !). As a second generation refugee it was quite common for them to use a mix of both Huguenot chapels and the Anglican church, and I believe it's likely in that 9 year gap between these two confirmed children, your John Larcher, and his brother Andrew Larcher II, and likely other children besides, were also born to them and baptised in the Wandsworth Huguenot chapel, the records of which are sadly now lost to us.
Andrew Larcher I, was described as a Felt Hat Maker on his wedding 1735, his fathers trade, but I doubt he continued on that once in East London. He more than likely became a weaver there. The Wandsworth Huguenot community was tiny and very self enclosed by comparison, and it may simply have been there was not enough work for both father and son to ply that trade. In contrast the Silk Weaving trade just over the water employed thousands and was at the very height of it's success in the 1740's, and was dominated by the French refugees at that time, in a way it never would be again before or since. New Inn Yard was on the edge of Shoreditch and more or less in effect part of the adjacent Spitalfields weaving hub, where French was the common language for most.