I am not sure if this helps but one of my relatives was a tailor in Lincolnshire but I have not found an apprenticeship record. I think his father may have been a tailor and so learned from him.
In 1841, Robert was living in Alford where Rossiter Smith was a tailor.
Checking through the records, Rossiter had no son of that name but he had a sister, Mary born in 1790.
The only record that matches Roberts birth in Spilsby is Robert Brackenbury Smith born to Mary Smith, a spinster. Mary also had a daughter in 1818, Mary Brackenbury Smith. Perhaps Rossiter was Robert's uncle?
Unfortunately, Lincstothepast seems to be missing the marriage records of the period when Robert probably married.
David