I assume you have George's father's name as being George from his marriage cert? And Jane as his mother from the 1841 census which shows Jane 30, Emma 4 and George 13.
I'm always suspicious when children are out of chronological order in censuses, particularly in 1841 where relationships are not given. I wonder if George was really Jane's son or whether he was a lodger in the household - a nephew perhaps. (later - on rechecking the image there's a single slash after Emma, denoting the end of that particular family, and a double slash after George denoting the end of that house, so the enumerator was indicating that George was not the same family as Jane and Emma)
If you check the IGI on
www.familysearch.org there's only one George Allen in Barton, baptised on 8 June 1828, the son of George and Sarah. So the father's name matches the George which you have, and the year is right. It's the mother that doesn't match what you think it should be.
There's a marriage on 5 Jan 1833 at Barton, John Allen/Jane Blindell which I think is the Jane in 1841. The only burial in Barton of an adult male 1836-41 is John aged 38 on 18 March 1840. Jane's remarriage cert to Crawley would show her maiden name which would confirm what I suspect.
So I'm certain that Jane wasn't George's mother at all.
Living 2 doors away from Jane in 1841 was
George Allen 30 Carpenter
Sarah Allen 30
William 10; Albert 8; Elizabeth 5; Edwin 3; Leonard 2 mths
All born in Beds
I think these were George's parents and siblings.
Perhaps George had moved in with Jane (possibly his aunt) to make room for the new baby.
In 1851 both Georges were living in Luton
George Allen head marr 45 former carpenter b Barton
Sarah Allen wife 42 b Streatley Beds
Elizabeth 16; Edwin 13; Leonard 10; Emily 7; Edward 4. All b Barton
But I can't see a marriage on the IGI for George and Sarah, which I assume should have taken place in 1827/8
Regards
David