Hi Andrew,
welcome to this great site from across the water. I see you're in Weston Super Mud as I'm afraid we used to affectionately call it on our regular family day trips. Nowhere else could the phrase "lets go for a quick paddle" instill such leg-fatigue into small kids ! ;-), the tide being invariably out "for lunch" by the time we'd arrived from the Forest.
First may I remind you what I'm sure you know, that Abercarn is someway outside of the Forest of Dean area so is not within this site's remit or PR database.
http://www.forest-of-dean.net/?About_the_Forest

Abercarn is within this Parish
http://www.genuki.org.uk/big/wal/MON/Mynyddyslwyn/#Description

Clearly the Forest does have traditional links with the South Wales valleys and it's iron & coal industries so I have had a quick search for the Marriage via FreeBMD, have you tried this excellent free site, if not I strongly recommend it. I believe it has decent coverage of the South Wales area where I expected to find your Marriage, however that said the nearest I've found thusfar is:

Surname First name(s) District Vol Page
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Marriages Jun 1890 (>99%)
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Parnell John Doncaster 9c 726
PHILLIPS Alice Sheffield 9c 726
Spencer Mary Elizabeth Sheffield 9c 726
Taylor Mary Frances Sheffield 9c 726
TURTON Thomas Sheffield 9c 726
WIGLEY Henry Sheffield 9c 726

HOWEVER please search FreeBMD yourself in case this isn't our couple, don't be too over specific wrt first names and do try variations of spelling.

Does the Sheffield area tie in with your family, your query wasn't overly specific so I assumed I was looking for South Wales or Somerset PRs ?. If you can provide more background to the couple then we may be able to help you more too.

Of course the Abercarn area had an ironworks which is a clear link to Sheffield, although I suppose it is more likely to be remembered for it's coal mining history following the terrible disaster of 1878.
http://www.geograph.org.uk/photo/1539643

http://industrialgwent.co.uk/newbridge.htm

http://www.newbridge-online.info/collieries.html

http://www.gracesguide.co.uk/Ebbw_Vale_Steelworks

Regarding the above FreeBMD result, I tried searching for Births for the couple, there a re a LOT of Alice Elizabeth Phillips listed but I only find three Arthurs:

Surname First name(s) District Vol Page
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Births Jun 1858 (>99%)
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Parnell Arthur James Portsea 2b 326

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Births Mar 1883 (>99%)
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PARNELL Arthur James Thornbury 6a 218

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Births Sep 1907 (>99%)
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PARNELL Arthur James Ringwood 2b 694

On the face of it given your current address I'd perhaps target the Thornbury option, thinking of the Somerset coalfields (not to mention the wellknow Parnell aeroplane manufacturers at Yate, Bristol in the 1920s & 30s), which of couse doesn't match the Marriage. Again I await your further guidance please.

Hope this helps, J

Are there any Forest of Dean links, to your knowledge?

I see on Genesreunited - the marriage of Arthur James PARNELL and Alice Elizabeth PHILLIPS has not been found- do you have any approximate ages of this couple, i.e. from death records etc.

A daughter is listed as Florence Elizabeth PARNELL - born 1913 - Pentwynmaur, WALES

There is an Alice Phillips aged 19 daughter of Elizabeth(Widow) 1911 C High Street Abercarn

After 'some work' - this is not the correct Alice in Abercarn: and googling around found various peoples requests/research.

This is the marriage on Freebdm

Alice Elizabeth PHILLIPS married James PURNELL - 1907 - Thornbury District
Alice Elizabeth PHILLIPS born - 1880 Thornbury District (which ties up with Alice & James birth/death) ***

so doesn't appear be the Forest of Dean - as they are both from Olveston (still there 1911 with two young children)

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This however, is the Alice on the 1911 census return, who's father was from the Forest of Dean

1901 Monmouthshire
Abercarn

PHILLIPS

Thomas - 49 - Haulier, below ground - born Monmouthshire Lydne
Elizabeth - 53 - born Carnarvon
Laura - 12 - born Abercarn
Alice - 9

1891 Census, Monmouthshire, Mynyddslwyn

PHILLIPS

Thomas - 36 - Coalminer, born Monmouthshire, Lydne
Elizabeth - 46 - born Carnarvon
William E DAVIS, stepson - 16 - born Rhonda Valley
Laura J PHILLIPS -2 - born Abercarn
Robert WILLIAMS, boarder - 22 - Coalminer, born Glos. Lydbrook

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PARNELL's deaths in Caerleon, Monmouthshire

***
Alice E PARNELL - 1938 - age 58 = birth c1880
James A PARNELL - 1842 - age 59 = 1883 (note christian names the other way round)

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Freebdm

births in Newport M - PARNELL/PHILLIPS

Florence - 1913
Doris - 1916
Lilian - 1919
Arthur G - 1922

and these 3 seem to have married in Caerleon, Monmouthshire