However Ann's parents weren't great fans of the future billionaire and thought she could do better.
"In her parents' mind I wasn't 'catch of the month'. It's the old thing of they'd rather have an accountant, a lawyer or a doctor," Alan said.
On 28th April 1968, two years after meeting, Alan and Ann tied the knot at London's Great Portland Synagogue but the proposal wasn't exactly the stuff of rom-coms.
"It was more along the lines of, 'I suppose we should get married then?'" the billionaire shared.
"There was certainly no going down on one knee, with a rose, in a restaurant. In fact we were going over the Stratford flyover in the minivan at the time."
The couple then welcomed their children Simon, born in 1969, Daniel, born in 1971, and Louise, born in 1974 and are now grandparents of seven.
Even when he started raking in the cash, Alan always put aside holidays, evenings and weekends for his family but never discussed business with Ann.
"I guess that I knew that she would not have anything to offer me other than to stop worrying and that was about it."
However Lady Sugar can read her husband like a book.
"The minute he walks through the door, I've only got to look at his face and I know whether he's had a bad day or a good day. When he's had a bad day I've never pestered him or asked him any questions. I knew that when he was ready to talk he would talk but I never knew anything about the actual running of the business or anything like that."
To celebrate their 40th wedding anniversary, Alan and Ann threw a lavish party at their home and the billionaire boss paid tribute to his leading lady.
"Ann always says that the day she met me she knew she had met Mr Right. What she didn't know my first name was 'Always'," he joked at the event.
However, even couples who have been together as long as Alan and Ann have their arguments.
A big one arose when the Celebrity Apprentice boss signed his wife's birthday card: "Best wishes, Alan Sugar."
"That will stick with me forever," he admitted after recalling the incident. "That's why I keep her away from newspapers and television cameras so she can't tell the story anymore!"
Ann laughed that she "went mad" when she saw the card and was "absolutely furious" with her husband.
"I got roses, he felt sick when he realised what had happened, he felt terrible."
Over 50 years on from saying 'I do' Alan and Ann are now Lord and Lady Sugar but the level of wealth they have now is something Ann never expected.
"I just thought that we'd be an ordinary, everyday family, didn't dream it would happen, what has happened," she said on The Real Alan Sugar.
As for Alan, he says Ann is "absolutely" the only woman he's ever love.
"I couldn't ask for a better wife than her. I'm still wondering what it is she saw in me... she must've seen that spark of genius in there that I have."