Would you believe there's a web site devoted to providing information such as this? It's called UK Television Adverts. It has a search function, and I was able to find out (besides what was posted above) that the ad was for Intercity, and it came out in 1999. Ain't the Internet grand!

But I found the words somewhere else:

SO, RELAX
(Leon Redbone & Beryl Handler)

(1) Anytime you choose, kick off your shoes.
Rest your weary eyes and catch up with the news.
A favorite book will be the perfect company,
So, relax.

(2) Forget about your blues. You're doing fine.
Leave your cares and worries far behind.
Loosen up your tie. Let the world speed by.
Relax.

(3) Life and all its troubles start to get you down,
Laugh and click your heels up and turn yourself around.

(Repeat 1, 3, 2)