Mr Nolan said: "A junior nurse came in and told me that the surgeon said I was too big for the table and he would not do the procedure.
"The surgeon did not even have the courtesy to tell me himself.
"I waited around at the hospital for a proper explanation but no one came to speak to me, so I went home.
"I am fuming. Over the past two weeks, I have made all my wishes known just in case I did not come out.
"As far as I am concerned, the Royal is a joke. I would be better off in a third-world country."
An angiogram involves a fine, flexible tube being inserted into the coronary arteries. Doctors can then take pictures and decide how serious the problem is.
A spokesman for the Royal said: "Mr Nolan's personal circumstances have changed since before Christmas, so his doctor and consultant will be writing to him."