"They turned up at my door at 8.20 a.m. and I had a taxi booked for half past eight. I was a bit worried I was going to be late but the taxi did a great job in getting us here," he said.
"It's part of the job but when you have a day like today you are looking forward to, it's the last thing you need."
The 26-year-old tennis player was due to receive and Order of the British Empire from William the Duke of Cambridge.
"He asked me about my back surgery which I had a few weeks ago and how I was feeling after Wimbledon, when there a lot of pressure on me," Murray said of William.
"I teased him a bit as he had sent a note to me before Wimbledon wishing me luck and his wife had written me a letter afterwards. Her handwriting was beautiful and I told him how fantastic it was compared to his."
Murray was awarded the OBE in the New Year Honors, before his triumph at Wimbledon, after winning the US Open and Olympic gold medal in 2012.
The ceremony was supposed to last 60 minutes but it extended to an hour and 25 minutes as William spoke to some of the recipients for more than a minute. William's grandmother, Queen Elizabeth II, usually adheres to 30 seconds per recipient.
"I have met him a few times before and he has always been very easy going," Mueeay said of the Duke. "He seemed very relaxed today."