Officers suggested the 2007 case bore hallmarks of a "pre-planned abduction".
Scotland Yard said it was also looking into possible links to burglaries and bogus charity collections in the area.
Crimewatch editor Joe Mather said several callers gave the same man's name after e-fit pictures were shown.
Madeleine, from Rothley, Leicestershire, was three years old when she disappeared from her parents' holiday apartment in Praia da Luz on 3 May 2007.
Police outlined their latest findings in the search for Madeleine on BBC One's Crimewatch on Monday.
Detectives released two e-fits of a man seen carrying a child in Praia da Luz at 22:00 on the night Madeleine went missing and it was revealed that police now suspect Madeleine could have been taken later than previously thought - just before her mother returned to the apartment to check on her.
In an update, Det Ch Insp Andy Redwood, the senior Metropolitan Police investigating officer, said there had been 730 phone calls and 212 emails "as a direct result of the specific lines of enquiry we issued yesterday".
"Detectives are now trawling through and prioritising that material," he said. "This will take time."
Crimewatch's editor said the appeal "went better than expected" with many of the calls received from British people who had been at the resort at the time but had not previously contacted the Met.
Mr Mather told BBC Radio 4's Today programme a number of different names for the "key 10pm sighting" were mentioned and several callers suggested the same name.
Clickable map and timeline
Det Ch Insp Redwood told Crimewatch a number of men had been seen by witnesses in the area on the day Madeleine vanished and one theory was they could have been carrying out reconnaissance.
He said they wanted to track down men seen "lurking suspiciously" near the McCanns' apartment block.
The Metropolitan Police say their inquiries have led to the timeline and "accepted version of events" surrounding Madeleine's disappearance being significantly changed.
Det Ch Insp Redwood said it had been a "revelation moment" when police discovered a man seen by the McCanns' friend Jane Tanner at 21:15 was almost certainly an innocent British holiday-maker collecting his two-year-old daughter from a nearby creche.
He said: "Our focus in terms of understanding what happened on the night of 3 May has now given us a shift of emphasis.
"It takes us through to a position at 10pm when we see another man who is walking towards the ocean, close by to the apartment, with a young child in his arms."
Crimewatch featured a detailed reconstruction lasting close to 25 minutes.
The film is also to be shown in the Netherlands, Germany and Irish Republic this week as tourists from those countries were known to be in the resort at the time.
Det Ch Insp Redwood said he would be travelling to the Netherlands and Germany to continue the appeal.
Madeleine's parents Kate and Gerry told the programme they were "hopeful and optimistic" after the fresh appeal for information.
Mrs McCann said: "We're not the ones that have done something wrong here. It's the person who's gone into that apartment and taken a little girl away from her family."
Inquiry timeline in full
The two e-fit images released are of a man a family had seen with a blond-haired child of three or four, possibly wearing pyjamas, heading away from the McCanns' holiday apartment.
Det Ch Insp Redwood said he could be the man who took Madeleine - but there could be an innocent explanation.
He also said there had been a four-fold increase in the number of burglaries in the area between January and May 2007 and one possible scenario was that Madeleine had disturbed a burglar.
Police are also looking at possible bogus charity collectors operating in the area at the time and have released two e-fit images of Portuguese men they would like to identify.
Police have also released e-fit images of two men seen in the area around the time that Madeleine disappeared. Two are of fair-haired men who fit similar descriptions.
Portuguese police shelved their inquiry in 2008 but Scotland Yard began a review of the case in May 2011 and opened a formal investigation in July this year.
BBC News correspondent Tom Burridge in Praia da Luz said Portuguese police have not commented on the Met investigation but have given the impression that they are co-operating well with their British counterparts.
Mark Williams-Thomas, a child protection expert, said it was a "pity" there were no plans to show the Crimewatch appeal in Portugal.
"There are a lot of residents there who may have information," he told Today.
He suggested further progress in the case required Portuguese police to reopen their investigation.
Madeleine and her brother and sister were left in the apartment at 20:30 while her parents dined with friends at a nearby restaurant.
Mr McCann checked on them at 21:05 and Mrs McCann raised the alarm at 22:00.
In the programme, Mrs McCann described the moment that "panic kicked in" after returning to the apartment to find her daughter missing.
Police probing the disappearance of Madeleine McCann in Portugal say there was an "overwhelming response" to an appeal on the BBC's Crimewatch, with almost 1,000 calls and emails.