Harry ap Harry (ap meaning son) became Harry Parry following a decree many centuries ago that everyone had to have a surname thus many added an S onto there names William Williams Hugh Hughes etc
If it helps, there is no "K" in Welsh, but there is in Cornish. Also, I found this doing a quick Google search: http://cornishcrier.com/nwsltrs/cc_vol14_no3.txt
It's a long page, but open it, then click your "Find" or "Find on Page" button--mine is under my "Edit" button and type in "Tredick"--it just appears i a long list of Cornish surnames, but maybe by reading more of the page, you'll find more clues, or just r-Google.
Keep us posted.
Back in the 1880's, a Tredick relative went to London to try to track the name down. He went to the Coat of Arms library and could find nothing. The gentleman at the Coat of Arms Library thought the name was from Cornwall also. My relative stated in a letter that he would go to Cornwall on his next visit to England but died before he could travel back to England. So that falls in line with Neil's thought.
Wallace Tredick Parry
My great grandfather, Thomas TParry,his wife Ann Jones, and his father Thomas Parry, left CAERWYS, FLINTSHIRE around 1840 and sailed for America. I know that Parry is Welsh, but my middle name is Tredick. I thought for years it was an English name, but when my grandson, whose middle name is also Tredick, went to day care, the lady there said it was Welsh. She is Welsh and she said she has seen the name Tredick many times in Wales.
HenryTredick, who I am descended from, arrived in Portsmouth, NH sometime prior to the 1740's but I don't know where he came from.
Any help would be greatly appreciated.
Wallace Tredick Parry http://ecuecu66.tribalpages.com/?userid=ecuecu66&x=11&y=7