There were two George Thompsons born in Amersham in 1837 & 1839, the later has a GRO index in 1840 but the former I think was born before registration began in Q3/1837. So I assume he was the one.
He was baptised 19 July 1837 parents Joseph Henry Thompson & Jane.
His father was the Blacksmith in Amersham, George is with the family in 1841 High Street, Amersham & 1851 Wildon Street, Amersham.
Regards
Colin