Is your Robert Birch/Burch, the one born Andover Hampshire (a chimney sweep in Wilts County Gaol, Fisherton Anger, in 1851 HO107/1846 Folio 461 Page 43 and a general dealer, in a caravan, with wife Harriet in Frome, Somerset, 1881) If so, his birthplace is Andover on at least two censuses so that would seem a good place to look for parish records maybe?
Theres this family in 1841 -
Ann Burch 40 Y
Thomas 20 Sweep Y
William 15 Sweep Y
Ann 15 Y
James 15 Y
Robert 11 Y
James 9 Y
Betty 7 Y
Charles 5 Y
Richard 2 Y
//
Thomas Burch 80 Sweep Y
Elizabeth 70 Y
New Street, Andover, Hampshire
HO107/411/3 Folio 5 Page 5
Regards
Catherine
