Hi Tony,
Looking at the parish records for St Nicolas Church (for elimination purposes) this is what I have found:
Checked baptisms 1799-1822: No Moulding children with mother Mary Moulding (apart from George Leander Moulding in 1813) found.
Checked baptisms 1780-1790: No record for a Mary Moulding found.
Checked marriages 1799-1812: No record for a male Moulding to a Mary ? found
so it looks like the Mary Moulding in the 1815 census is George Leander Moulding's mother.
Whilst I was looking at the baptisms for 1799-1812 I did find this baptism (I obviously missed this one when searching the records before):
Name: John Mayo
Born: 22nd Aug 1809
Bapt: 13th Sept 1809
Parents: John and Mary Mayo
Which closes the gap a little (between 1807-1813).
Presumably this John died before 1816. (when John number 2 was born). I did look for a death/burial for both this John and one for Robert born 1807 (unlike his siblings Robert doesn't appear in any records other than his baptism) on both the NBI and the BBI but couldn't find any.
With regard to Northbrook Street, there are only about 50 shops/houses on both sides (as per Newburychap's post on page 10) and the population of Newbury in1815 was 5,309 so it's highly likely that the Mayo and the Moulding families would have known each other. Perhaps John Totty Mayo popped into the George & Dragon for a drink or two.

(coincidentally my ancestors moved to Newbury and held the license for the George and Dragon from 1929-1953)
In the 1841 census John, Mary and their son Thomas Totty Mayo were recorded living in West Mills Newbury, this road ran down the north side of St Nicolas Church see here:
Link to google maps (If you swivel the picture around you can then travel down the road and see what West Mills looks like today) :
https://www.google.com/maps/@51.4010224,-1.3253692,3a,75y,84.65h,99.29t/data=!3m6!1e1!3m4!1snmO-g6rFEo_lxADfvFLeKw!2e0!7i13312!8i6656in the 1851 census John and Mary are recorded as living in Raymonds Almshouses there are two Raymonds Almshouses in Newbury, Lower Raymond (built 1796) and Upper Raymond (built 1826)
Pictures of Lower Raymond Almshouses:
https://www.onephotographaday.org.uk/the-lower-raymond-almshouses-newtown-road-newbury/Pictures of Upper Raymond Almshouses:
https://britishlistedbuildings.co.uk/101210612-upper-raymond-almshouses-newburyBoth of these Almshouses are still standing and in use today. I can't be absolutely sure but looking at the 1851 census I would favour the Lower Raymond Almshouses as the residence for John and Mary as looking at the census pages they seem to record the Raymond Almshouses then Newtown Road .
Here is a link to Newtown Road which shows you Lower Raymonds Almshouses as they are today:
https://tinyurl.com/y5ukmqytIf you swivel the picture around and then travel forward along the road up to the roundabout, go all around the roundabout and then travel down the road marked no entry (Derby Road) half way down on the right you should see a patch of grass with cars parked on there, beyond the cars is Upper Raymonds Almshouses
If you go back to the link (below) swivel round and travel back to the roundabout and then go straight across (taking the 2nd exit (Newtown Road) then travel along the road a little way you should see a cemetery on the right hand side, this is where John Totty Mayo was laid to rest:
https://tinyurl.com/y5ukmqytHere is a link to Friends of Newtown Road Cemetery where you can view the record for John Totty Mayo (other Mayo's recorded also)
http://www.fnrcnewbury.org.uk/index.asp Best Wishes
Chris