"I was so influenced by them that I decided from an early age that that is what I wanted to do, to be a performer, to make people laugh," said Williams.
"I became an actor at the age of 15, joined a Rep theatre company and learnt my craft. Twenty seven years later, I'm playing my hero, a genius and a true comedy legend."
He added: "The difficulty in being Tommy Cooper is mastering the scenes when Tommy isn't performing, when he's being himself. There are no recordings of him when he isn't 'Being Tommy Cooper'. He was always 'on'; playing up to the camera and never gave anything of himself away.
"There is one documentary called "The Untold Tommy Cooper" where they are talking to him and you can see he is tired. They say 'this must be exhausting', and there is one line where he says 'yes, it is' where he is not being Tommy Cooper.
So I have this one sentence to work out what he's like when he's not being Tommy Cooper. Because whenever he was on telly, in interviews or performing he was always being Tommy the magician and entertainer."
In preparation for the role, Williams visited the place of Cooper's death - Her Majesty's Theatre - on the anniversary of the comedian's death. Williams described the experience as "a weird feeling" to walk in the same stage door that Cooper walked in that night, entering from stage left, the same side the comedian entered and standing in the middle of the stage where the star stood for the last time.
Goosebumps, hairs standing on the back of my neck, shivers. I experienced them all standing there," said Williams. "A member of the crew appeared and said "That's where he died", pointing to the prop store stage left, "they dragged him into there, and that's where he died".
I followed the crew member into the tiny room and just stood there trying to look for signs of Tommy. Of course there weren't any."
Getting back to the play, Williams explains that it is very truthful, "about his dark side as well as his genius, and that's what's great about it - you get the whole story".
"It's a great night out as you get all the laughs but there's also a side of him that nobody knew," adds Williams. "There are things about him that I didn't know until I'd read the script, that the writer Tom Green had found out. So it's a fantastic play."
Tom Green's plays also include The Death Of Margaret Thatcher, at the Courtyard Theatre, and radio plays including For Ever England and The Tent, both for BBC Radio 4.
The play, which stops off in Birmingham as part of a 39-date national tour, is not suitable for anyone under the age of 14.
The performance is 1h 20mins long.
Being Tommy Cooper
Birmingham's New Alexandra Theatre
June 12 at 7.30pm
Tickets cost £13.90 - £27.90
from Theatre Website