Dodgeson and Hutchinson - Northumberland

[Neale1961]

Mary married George  Coxon and around 1843 .

familysearch have their marriage as 16 April 1843
https://www.familysearch.org/ark:/61903/1:1:QP74-6GCY

See this thread related to Coxon
https://www.rootschat.com/forum/index.php?topic=841195.msg7074409

[Neale1961]

Baptisms for children of Timothy and Ann Dodgson in Newcastle:
Elizabeth 1813
Anne 1815
Timothy 1818
Mary 1820
Margaret 1826
Thomas 1827
Edward 1830
James & William 1833

[Neale1961]

From information in the census we suppose Ann (Hutchinson) Dodgson was born about 1791 in Northumberland. According to the OP and various transcripts of the 1861 census, her place of birth might be Harnton MILL or Harnton HALL or Hampton HILL  - I cannot find any of these.
I think it is more likely to be ‘mill’,  rather than a ‘hill’ or a ‘hall’. I wonder if someone with access to the original census page might see what it looks more like.
The most likely mills I can find would be Haughton Mill (near Barrasford) or Halton Mill (near Corbridge)

[maddys52]

Here is a snip of the 1861, I agree - it looks like Harnton Mill

Oh, I can't attach on a lookup request, but it does look like "Mill"

The 1841 census definitely shows born Scotland, so perhaps the place is very close to the border?

[maddys52]

I've put a snip of the name on the handwriting decipher board.
https://www.rootschat.com/forum/index.php?topic=841229.new#new

[Neale1961]

Here is a snip of the 1861, I agree - it looks like Harnton Mill

Oh, I can't attach on a lookup request, but it does look like "Mill"

The 1841 census definitely shows born Scotland, so perhaps the place is very close to the border?

There is Heaton Mill near Crookham, which must be close to the border.

[maddys52]

I can't see any reference to Harnton Mill, there is  a mention of a "Harnton Hill" in 1886 (a bankrupt butcher "lately of Gateshead ..., now of Hope-street Harnton Hill" 

[Neale1961]

Here is a snip of the 1861, I agree - it looks like Harnton Mill

Oh, I can't attach on a lookup request, but it does look like "Mill"

The 1841 census definitely shows born Scotland, so perhaps the place is very close to the border?

There is Heaton mill near Crookham in the north east, near the border.

[Neale1961]

i found a reference to Harnton Hill in Durham Thornaby.

Edit. 1851 census
https://www.familysearch.org/ark:/61903/1:1:SG69-LH4

Baffling!!!