Julia , I haven't been able to find Edward on the 1851 census but in 1841 he is with his mother in cheltenham
he was in fact born in dudley
1841.
Harriot Beesley age 30 Tailoress not born in gloucs (in further census she says born Eckington Staffs.
Emma beesley age 7 not born in gloucs in further census she says born Dudley.
Edward age 6 not born in Gloucs
Henry 2months b cheltenham
their father Henry Beesley died in cheltenham Dec 1840.
Henry Beesley married Harriett Haywood ,21st june 1832 St Martins Birmingham.
Emma Haywood Beesley baptised St Thomas dudley 5th October 1834 parents Henry and Harriett.
Edward Fort Beesley born 27th June,1835 baptised 7th May.1837 st Thomas Dudley parents Henry and Harriett.
There was a daughter Sarah Beaumont Beesley born 28th Jan 1837 baptised on the same day as Edward.parents henry and Harriett
She is not on the 1841 census and there is a death of a Sarah Beesley in Cheltenham in 1838.
Edward Fort Beesley married Amelia Elizabeth Smith ,25th August 1858 St Martin Birmingham(although the BMD index has him as Edward Frederick)
1861 Sherborne street
Edward Beesley age 25 b Cheltenham , Baker (i suppose that Edward would have thought that Cheltenham was his birthplace. having lived there from childhood)
Amelia age 20 b Birmingham
Edward Henry age 1 month
Henry Beesley age20 b Cheltenham , brother, Baker