My great Grand dad Samuel Worrall was Mayor of Cwbridge, South Wales.
I am tring to find a record?

I expect that you mean Cambridge, NSW.  This genealogical site may be of help  
http://www.ihr.com.au/

Several Worralls ?as you probably know ? can be found on the web, 
Having one like George from the 1820s in Australia in your family tree
is not quite ennobling, but no smirch to the name, in Australia  ;)

http://www.travelmate.com.au/Places/Places.asp?TownName=Campbelltown_%5C_NSW

A satellite city in Sydney?s south-west, Campbelltown is one of the
few towns which has converted murder most foul into a festival art
form. The town celebrates the Festival of Fisher?s Ghost every
November, and several other institutions and local businesses have
hitched their stars to the spectre of petty villain and murder victim
Frederick Fisher. Fisher made one supernatural appearance - four
months after his last mortal sighting on June 17, 1826. As local
farmer John Farley rode by, the ghostly form of the missing man sat on
the rail of a bridge, pointing to a nearby paddock. In November, 1826,
Fisher?s remains were found in the paddock and, subsequently, his
former neighbour George Worrall was hanged for his murder.

Thank you, 
Sorry I meant Cowbridge, South Wales, Britain. My great grand-dad
Samuel Worrall was Mayor in or about the late 1800's.  I am trying to
find some record.

I haven't heard of this george but the satory is interesting, I will
keep it in mind as I research William Worrall and backwards since I
know nothing beyond Williams birth. Who know's a relative may well
have gone to Australia some of my mothers side did, and to New Zealand
but in the 1920's.

Sorry, I went off halfcocked, jumping to Australia when I read South
Wales, having lived in NSW for a couple of years.
Back in the old country, they probably tried to forget someone "transported".

The Glamorgan Record Office

http://www.glamro.gov.uk/

http://www.glamro.gov.uk/contact.htm

should have several records, such as the "declarations of oaths by
Mayors of Cowbridge, 1894-1926"
http://www.glamro.gov.uk/news8.html


"The Council Chamber has ... boards listing past Mayors, Town Clerks
and Honorary Freemen":
http://www.cowbridge-tc.gov.uk/abtcouncil.html

"Queen Victoria granted the last Royal Charter in 1886 which allowed
the people of Cowbridge to elect their own Councillors and Mayor":
http://www.cowbridge-tc.gov.uk/abtcouncil.html

http://www.cowbridge-tc.gov.uk/contact.html

You can depend on Fp-ga, while I was vicariously reliving times Down
Under, she (?, why do I thing so?) was barking up the right tree (a
southern US expression from raccoon hunting).