From TV series, Trigger Happy Tv CH.4, there is a song from the
soundtrack that I want to trace the artist's name. Opening line ..."
If you could read my mind ...." Sounds very much in the style of James
Taylor but can't be sure.

Hello Spacer,

Thank you for your question.

The name of the artist who sings ”If You Could Only Read My Mind” on
Trigger Happy TV on Channel 4 is Gordon Lightfoot.

At the Gordon Lightfoot Discussion Forum I located this thread.
“I have been watching Trigger Happy TV recently on Channel 4 in
England. Each week, a backing track comes on and by the power of the
internet, I have found out that it is "if you could read my mind love"
by a certain Gordon Lightfoot.”
Gordon Lightfoot Discussion Forums Website
http://www.corfid.com/ubb/Forum1/HTML/000055-3.html

Lyrics of “If You Could Read My Mind” by Gordon Lightfoot
http://gordonlightfoot.com/Lyrics/IfYouCouldReadMyMind.html

You can hear “If You Could Read My Mind” at Andrews Trigger Happy TV
Page.
http://www.andrewswebsiteuk.co.uk/files/ifyoucouldreadmymind.MP3

Gordon Lightfoot Biography 
Gordon Lightfoot Website
http://gordonlightfoot.com/GordonLightfootBiography.shtml

An article about Gordon Lightfoot: ”Master Craftsman of Popular Song”
by Nicholas Jennings
Rhino Records Website
http://www.rhino.com/Features/liners/75802lin4.html

Search Criteria:

"If you could read my mind * " +trigger happy
://www.google.com/search?sourceid=navclient&hl=es&q=%22If+you+could+read+my+mind+%2A+%22+%2Btrigger+happy


I hope you find this helpful and if any part of my answer is unclear,
please don't hesitate to ask for clarification before rating it.

Best regards,
Bobbie7-ga

Great job done...much appreciated!