Anne Barnet, (b. 1760) married John Roberts, (b. 1760)

[Daltonator86]

it shouldn't make any difference to searching if the name has one or two ts! Spelling wasn't consistent at the time, so you need to look for variants.

The baptisms at Dymeirchion mentioned by jonw65 for give Ann's name as formerly Barnard on Edward's and formerly Bernard on Robert's.

There's a marriage in Cwm in 1765 for an Edward Barnet as written by the vicar but Edward signed Barnad.

Although I can't see a baptism for Ann as yet, there are Barnet baptisms in Cwm that could be relatives
to William & Elizabeth (Hughs) - marriage 27 July 1731
Elizabeth bp 23 April 1732
Katherine bp 21 April 1734
Elizabeth bp 22 May 1738
William bp 30 June 1742
William  bp 19 June 1743
Robert bp 24 Feb 1748
Ellin bp 22 May 1752

There are earlier ones to Thomas & Mary.

That could be well the case! The plot thickens, although once again, Ann's name is sparse....

[Daltonator86]

Would there have been many English in Denbighshire at that current time? I know that a lot of minesr from Derbyshire came to work in the mines in Halkyn but that's still a decent distance...
What if it is an Anne Bernard, which is far more of a (Norman) Welsh name....

It wasn't unusual for migration into Wales at that time. Two of my lines moved into Denbighshire from bordering English counties - Shropshire and Cheshire - in the mid-1700s. Again, another line moved from Kirkcudbrighshire to Denbighshire in the 1830s. This family came by boat via the Irish Sea  and landed at Kings/Queensferry.

Also, the marriage entry is definitely written as Barnet. I've not checked the license.

Tremeirchion is not far from Cwm.


Gadget

BTW, as you said when you had ancestors that moved across the border in the mid-1700s, what part of Denbighshire did they move to? Taking into account travel at that period in time and geography, villages were pretty isolated as far as I am concerned.