OK Andrew, Challenge accepted!
I write for magazines here in the UK, including a genealogy one - I know from experience "John Turner" is not a fun name to trace in the 19thC censuses!
And I was being lazy, hoping you knew the answer. So I went to look just now.
Civil registration of births marriages and deaths only started in 1837 so Turner is born too early for us to be certain which John Turner born in roughly 1821-24, he may be. There are a lot of John Turners. But I think he is the one born to John and Ann Turner, born 7/7/1823 at Fordrough St, Bham, son of John and Ann, John a "Pearl Button Turner", christened on 18/8/1823 at St Philip's. Fordrough St was apparently, right in the town centre - Aston, I think (no longer there?)
The first UK Census was 1841. I think I found him if he is John Turner, son of John and Ann Turner - pearl workers, Newhall St. (Bham city centre). St Paul's, enumeration district 7. The address appears to be "courts" or tenements. John's age is given as 18. Interestingly he is on the page of the census after "John Mitchell, Steel Pen Maker" who lives with a large family and several servants, also on Newhall St (and clearly not in a tenement!) They live a few doors down from eachother on a very populous and rather mixed looking street. I'd be surprised in Turner didn't work for Mitchell at this point (1841) - he's much closer than Gillott. There are steel pen workers down the street - almost all women.
Also I see online that John Mitchells produced Esterbrooks in the UK... On Newhall St. So I suspect Turner has links with Mitchell.
I did find the wedding certificate of a John Turner and Eliza Ward - from 5 years after the census - that are likely to be our targets. His job is "Toolmaker" and his father was also John Turner, a "Pearl-button maker". At time of marriage John lived on Coleshill St. Eliza Ward was from Garrison Lane and her father was Collingwood Ward, "A Gilt Toy-maker". They both can sign their names. They marry 26.10.1846. Coleshill St is according to Get Directions, a 23 minute walk to Graham St, where Gillott had his factory. Although maybe Turner was working elsewhere, by 1846.
The John and Eliza Turner of roughly the right age I pulled up for Bham in the 1851 census - were not them. (I'd already seen this couple's marriage certificate - different occupations although he worked with metal, too). I can't find our's at all on the 1851 census - it could be they are travelling - maybe back to France - or just been so badly mistranscribed they are hard to find (This does happen occasionally). They could just be in another city or town but so many John Turners it might take a very long search to find them! It's possible with his skills he was somewhere else in the Black Country (other counties around Birmingham that were the epicentre of metalwork in the 19thC - so much so, the hills and buildings turned black from pollution of the coal fires).
In other words: I can't yet find him in 1851.
Contrast him to Joseph Gillot who is very easy to find - distinctive name. On the 1841 Census he is living in posh Edgbaston on the Hagley Rd (very fancy, large Georgian houses - I know this place well as I went to university near here, and even lived for a while in a student halls of residence named after Josiah Mason!)
Enumerator's handwriting not exactly Copperplate! But I think Gillott is described as "Steel Penmaker" or it might be a contraction for Manufacturer". His neighbours are veterinary surgeons and merchants. Totally different world to central Birmingham, and Newhall St! We know Gillot and his wife, Maria are not from Warwickshire with the simple "N" for whether born in county or not. He has three servants.
1851, the Gillots are still in Edgbaston, but on Westbourne Rd. This enumerator has better handwriting as I can see that he is "Steel Pen Mfr". Joseph and his wife are from Sheffield here in Yorkshire. The Gilotts are very easy to find - Turners, not so much. By the 20thC, Bham would be England's second city so it is always going to be needle in haystack finding someone with this name, born pre registration!
I can't be confident the John and Eliza I found are our ones... I thought they'd be more easily findable by looking for Rosina as it's an unusual name even for the date, but drew a blank entirely on her. I found a number of John Turners born in Birmingham around the right dates but couldn't be sure which was him, if any. If he was a Non Conformist, those records exist but can be patchy. Looking for someone born around these dates, just before birth registration, your best bet is to hope the older generation live with the younger - then you can find them and trace back further. Although I think I struck lucky with the marriage cert from 1846.
I looked on Ancestry, the IGI and Free BMD for Rosina and could no-one of that name born in 1847. This is after civil registration came in so it is inexplicable. As for 1851 UK Census - she isn't there, either. In other words - you draw a blank in all the usual places, for Rosina. Added to the fact I can't find her or her parents in 1851.
I have a number of ancestors/relatives who emigrated to the US and sent for family later - leaving them behind in the UK til they found their feet, abroad. So I thought maybe Rosina stayed behind. There are several Rosina Turners born in Bham (later) in 1853/4 but I checked them out on the 61 census (after our Turners are in the US) and found them with different families, different areas of the city and not recorded as say "Grand-daughter" or "niece" therefore not our girl. According to US records (which I can't access but can see a little of) her birthdate was given when she died as February 1847. Which would put her earlier than all the unrelated Brum Rosinas I found.
It's possible she was adopted from a relative before they left England? The Turners may also just be there on the census but mistranscribed, as often happens, so a search doesn't easily pull them up. Sometimes if I go look another day, I find the person. Searches aren't reliable.
I'm not finding them on Passenger lists but I only have UK Ancestry and they are possibly on the US side of Ancestry. I'll keep looking sideways for 1851. Often I find someone with a relative. But it's possible they were abroad for a while.
I only discovered they were on the same st as Michell because I always find my target then search surrounding areas for relatives/links and to get a feel for the area (from people's given occupations).