He told CNN was yelled at by Heathrow security staff to "get to the end the queue" and when he questioned what was going on was told "we don't know."
When he made it to the passport control for the EU, he found many of the desks unmanned, he said.
There was "no explanation, no apology. I felt I was treated like commodity, not a valued customer of the airport."
His experience at Heathrow compared very badly to the efficiency he saw at Berlin, Windebank said, and "will kill business for Britain unless it is fixed."
Alastair Campbell, the former Downing Street communications chief under Labour Prime Minister Tony Blair, tweeted Thursday: "If this is what Heathrow T5 border queue is like on an average Thursday Olympic athletes should think about coming soon."
He said European Union passport holders were waiting just under an hour to get through immigration control, while non-EU passport holders were queuing for as long as three hours.
Only three or four staff were on duty to process EU arrivals and three for non-EU arrivals, he said.
Politician Keith Vaz, who chairs the Home Affairs Committee, told the BBC that Immigration Minister Damian Green had been summoned before the committee to explain what was happening.
Moore said the agency would be ready for the extra demand expected during the Olympic Games.
"We are fully prepared to manage busy periods during the Olympics and will be implementing our well rehearsed plans."
Heathrow, one of Europe's busiest airports, is building a special terminal to be used by departing athletes and officials for the three days after the Olympic Games ends.
An extra 40,000 passengers are expected on August 13, the day after the Games finishes, compared with a normal day, BAA said in a statement.