I am quite puzzled by some of the co-incidences and overlaps in the records for Thomas and Susan CARLEN and their son Thomas, with the records for John and Susan(nah) CARLEN and their son John William.
Could you tell us what records you have for either Thomas the father or Thomas the son - I can see only the one record on the 1851 census?
Was John CARLEN, 47 (b abt 1793), the person pleading guilty at the Old Bailey on 6 July 1840 to forging 2 bills of exchange? This man was sentenced to 7 years transportation, (I cannot see a transportation for him but it's not unusual to be sentenced and kept in prison in UK) and in the 1841 census he is in the General Penitentiary, Millbank, Westminster, occupation: clerk, not born in Middlesex.
There is no mention of this man in the 1851 census but in 1861 he is with his wife Susannah, and son John William, as we have already seen.
I am inclined to think that there is a possibility that the 1851 entry for father Thomas and son Thomas is actually John, his wife Susan and their son John William using the forenames Thomas and Thomas.
My reasons, and they are only conjecture:
There is no birth registered for a Thomas CARLEN anywhere in England and Wales in 1845. There is a birth registered for John William in 1845 in Shoreditch.
In 1851 Thomas jnr's birthplace is given as City Road, Middlesex which is definitely within the Shoreditch registration district.
In 1851 Susan's birthplace is given as Hampton, in 1861 Susannah (husband given as John) also has the birthplace Hampton The ages of the adults, birthplaces of Thomas and John are consistent across the censuses also.
You say that Thomas jnr is a cousin of John William which implies that Thomas and John (the fathers) were brothers. It seems to me to be too much of a co-incidence that there are two brothers, both marrying a Susan born in Hampstead 1801 or a Susannah also born in Hampstead 1801, both producing a son born the same year in the same area of London.
Perhaps John used the name Thomas as he had been in prison or perhaps the census enumerator collected the name incorrectly.
There is also a daughter of John and Susannah - Fanny Susan(na) Burton CARLEN, b1832.
Do you want information about her?
Cheers, Judith