Over the past few weeks I've been trawling through newspaper reports featuring the meetings of The Bedford Harpur Charity for the children living in the Bluecoat Hospital on 1841 census. While I've found nothing for your Joseph Dawson being admitted into the Hospital there are a couple of snippets about him leaving the place.
As per Hertford Mercury & Bedford Reformer June 1843. Apprentices. That Joseph DAWSON be allowed to leave the Hospital & go one month on liking to Charles Bond of Northampton, plumber & glazier.
As per Hertford Mercury & Bedford Reformer July 1843. Apprentices. Ordered, that the following persons be bound apprentice, viz:- Joseph DAWSON to Charles Bond, Northampton, plumber.
He was still there in April 1846 as per Northampton Mercury ; County sessions. Charlotte Bond, wife of plumber & glazier in Abington Street said.....: Joseph Dawson, apprentice to Mr Bond, corroborated his mistress's story.
In those day apprenticeships last 7 years & he started age 14 in 1843 so he was a freeman in 1850, although his master Charles Bond died April 1848. When he married Elizabeth BULL in 1850, his occupation was painter. On 1851 census he was a painter, & on 1861 census he was a plumber.
Regards John