I haven't worked out for sure yet, but I believe it may well be this Henry Nash who was born during q3/1857 at Highworth District, Wiltshire, England. In the 1901 and 1911 census returns, he gave his place of birth as Swindon, Wiltshire, and the Highworth District included the town of Swindon.

The 1901 and 1911 census returns indicate that he went by the names of Henry and William Henry so it's not easy to trace him backwards through time.
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I believe this is Henry's family in 1901, living at Cold Ash, Berkshire. The age of Primrose is about right to have been Primrose Nash who married Albert Jenkins. I guess Aquilla would be William Henry Aquilla?:
Henry Nash 40 Swindon Wilts Berkshire Cold Ash Bricklayer
Alice Nash 30 Highclere Hants Berkshire Cold Ash
Primrose Nash 2 Newbury Berks Berkshire Cold Ash
Priscilla Nash 3 Newbury Berks Berkshire Cold Ash
Aquilla Nash 5 Newbury Berks Berkshire Cold Ash

Elizabeth Nash 45 Greenham Berks Berkshire Cold Ash Laundress

I believe Priscilla is in fact Alice Ivy P who was born Jul-Sep 1897 at Newbury District, and Aquilla is William Henry Aquilla.

So far, I've not been able to link back to Henry's parents.
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We see Henry Nash at the 1911 census return with his wife and famly living at 2 Prospect Place, St Johns Road, Newbury, Berkshire:
William Henry Nash head 53 married Hawker or Dealer (Miscelaneous) Own Account Swindon Wilts
Alice Nash Wife 40 Married Highclere Hampshire
William Henry Acquilla Nash Son 15 Single Butchers Errand Boy Newbury Berks
Alice Ivy Priscilla Nash Daughter 13 Newbury Berks
Ellen Sophia Primrose Nash Daughter 12 Newbury Berks

The census also shows that Henry and Alice had been married for 16 years and had three children in total.
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The family story is that the Nash family came from North Wales and that they gave up their home and moved to Caergwrle in Flintshire, Wales to care for an elderly relative. However, my belief is that the family was originally living in Newbury in Berkshire, certainly at the time of the 1901 census.

The two daughters we can see living at Cold Ash (which is near to Newbury) were known by their family names of Nellie and Cis. I heard from their neice Dorrie, that Nellie married a man named Albert Jenkins. She died in 1933 at the age of 33. Dorrie also knew Cis as Alice, and that she married a man named John Palmer. Unfortunately, Dorrie only knew Nellie as Nellie.

My research shows that a Primrose Elizabeth ("Nellie") Nash married a man named Albert Jenkins in Hawarden District of Flintshire in 1919. I also found that she died in 1933 aged 34. Albert Jenkins was actually born in Caergwrle.

I also found that an Alice Ivy ("Cis") Nash married a man named John Albert Palmer at Hawarden District, Flintshire.

I am therefore convinced that this proves almost conclusively, that the Primrose, and Alice Nash we can see in Cold Ash Newbury are the same ones who married in Flintshire.

My belief is that the family all moved from Berkshire, England to live in Flintshire, Wales at some time between 1911 and say 1913/1914, but the reason why they moved has yet to be identified. I suspect that the story passed down through the family is partially correct and that they moved from Berkshire to North Wales (not the other way around) to care for an elderly relative? Nash didn't seem a common name in that area at that time.
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One possibility I can see is in the 1901 census, there is what appears to be a single mum called Annie Nash living at a place called Llandanwg, Merioneth, Wales. Merioneth is in North Wales and close to Flintshire. At the time she had a young child Henry William Nash living with her. In 1910, we can see an Annie Nash died in Hawarden, Flintshire (the very same district that Primrose and Alice Nash were married and also, where Henry Nash and his wife Alice Maude Nash later died themselves). Annie was just 44 when she died so her son would have been about 10. I wonder if this incident is related at all? Was Annie perhaps Henry's sister? Was she a widow? Were there perhaps elderly relatives who had depended upon Annie for support? This is however pure speculation.
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Another possibility is that in 1901, we can see an Arthur F Nash living at Llandudno in North Wales, around the coast from Flintshire. Arthur F Nash gave his place of birth as New Swindon, Wiltshire - Henry is from Swindon, Wiltshire. Was he perhaps Henry's brother?

The details recorded for this Arthur in 1901 (in case it's of value later) were:
Arthur F Nash Head Mar 32 Ironmongers Book Keeper Wiltshire New Swindon
Sarah J Nash Wife Mar 33 Lincolnshire
Frank Nash Son 7 Lancs Manchester
May C Nash Daur 4 Lancs Manchester
Wilfred Nash Son 1 Carnarvonshire Llandudno

Looking back in case this Arthur F Nash is connected, we see him in 1891, living in the household of George Cavil, a widower, at 15 Lark Terrace, Rochdale, Lancashire:
George Cavil Head Mar 48 Iron Moulder Swinfleet Yorkshire
Edith Cavel Wife Mar
Arthur F Nash Step-Son Mar 23 Clerk in Iron Works Wiltshire Swindon
Sarah J Nash Step-Daur 24 Lincolnshire Horncastel

Looking forward, we know that he moved to live at 147 Victoria St, Ashton Under Lyne, Lancashire:
Arthur F Nash Head Mar 42 Dairyman Wiltshire Swindon
Elizabeth Nash Wife Mar (2 years) 30 Assisting in Business Shropshire Shawbury
Frank Nash Son 17 Letterpress Printer Lancashire Manchester
May Charlotte Nash Dau 14 Assisting Dairy Business Lancashire Manchester
Wilfred Lionel Nash Son 11 School Carbarvon Llandudno
Frederick Nash Son 1 Lancashire Ashton U Lyne
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William Henry Nash died at Hawarden, Flintshire (Mold) HAW/18A/87