Their anxious presentations will be made to a steering group of sporting administrators who are due to deliver their final verdict on Tuesday - and with it will probably come more than pounds 100m of National Lottery money.
The object sounds relatively simple. What is required, by the year 2000, is one 80,000-seat stadium capable of hosting major sporting events.
Discussions have apparently been smooth and civilised, but there is no disguising the complex and potentially divisive nature of the steering group's task.
A central element in the whole process is The London Factor. The Sports Council stresses that this is not an Olympic bid, but a quest for a world- class British venue. That venue, however, must be capable of hosting events such as the Olympics.
Birmingham and Manchester have discovered in the last decade just how elusive those five rings can be, mounting three unsuccessful bids between them. The message which came down from International Olympic Committee circles on each occasion was that if Britain wanted the Games they would have to be in London.
The attitude was graphically illustrated two years ago when Sheffield was due to host the World Cup in athletics. The president of the International Amateur Athletic Federation, Primo Nebiolo, gave it to be understood that he had somewhere more metropolitan in mind. The event was switched to the capital.
The preference of the world's sporting grandees for somewhere glamorous, even the preference of their wives for major shopping possibilities, is a potent factor. Infuriating as it is to those outside the capital, such perceptions have to be acknowledged.
It is a message which steering group member Peter Radford reiterated last month. The British Athletic Federation's executive chairman, normally the most cautious of men, spelt out the fact that senior IAAF members would favour London above all other venues to host the 2002 World Championships, for which Britain will bid.
It seems clear that London cannot be without a major sporting facility. And for all the talk of Docklands sites and out-of-town locations near the M25, no alternative to Wembley has presented itself. "There is a lot of speculation in the media but not a lot from developers," a Sports Council spokesman said. "If there are any other bids out there, we haven't heard of them."
Hilary Kirkham, of the Brent Regeneration Agency, estimates that any new bidder would have to spend pounds 1.5 billion to match the infrastructure currently in place at Wembley - a sum which could be raised only by a direct grant from central government.
But the old Empire stadium, for all its unrivalled historical associations and mythical status, is not without problems. Parking space may be ample, but getting to it through the urban sprawl is a taxing experience.
The North Circular Road is currently being widened at a cost of pounds 100m; and London Transport is committed to rebuilding Wembley Park station at a cost of pounds 32m if the site is chosen for the national stadium.
Despite these improvements, some critics believe that there simply is not enough room around Wembley to host a major, multi-sport event. There would be none of the compactness which Birmingham or Manchester were able to propose to the IOC.
There are also doubts voiced about Wembley's plan to raise and lower the pitch hydraulically to enable those at the back of the stadium to see the athletics track, which will be revealed by removing the inner circle of seating. The exercise does bring to mind images of the Thunderbirds swimming pool; but Wembley maintains it is a thoroughly tested mechanism which is currently being used by oil rigs in the North Sea.
The British Olympic Association has announced its intention to bid for the 2008 Olympics and, if Wembley gets the nod on Tuesday, it must surely be the projected Olympic host. Thus Britain will be committed to bidding for an Olympics before being able to envisage how it would be accommodated.
The BOA has asked for the 31 October deadline to be deferred, but the Sports Council has kept to it - and there are no indications that the steering group will fail to choose one of the five bidding cities.
"We have been studying the bids in detail since 14 July," a Sports Council spokesman said. "So far they have met all the criteria. There are no major flaws. They are five abreast and coming towards us."
Manchester's charge is given impetus by the fact that they are due to have their hosting of the 2002 Commonwealth Games rubber-stamped on 3 November. The Sports Council is "absolutely committed" to assisting them in providing a suitable stadium for that event.
Both Manchester and Birmingham dispute the importance of the London factor, pointing out that recent major sporting events have been held outside capital cities - the 1992 Olympics in Barcelona, successive world athletics championships in Stuttgart and Gothenburg.
"The rest of Europe seems to be able to cope very adequately with having more than one major stadium," Howard Bernstein, the deputy chief executive of Manchester City Council, said. "No one is saying that London doesn't deserve a major sports facility. But why have you got to have all your eggs in one basket?"
Bradford, who plan to build the kind of ambitious, roofed creation of the kind inhabited by the Toronto Blue Jays or Ajax in Amsterdam, also acknowledge the need for a big stadium in the south-east, but insist that a northern stadium is also required. They are only asking the National Lottery for pounds 40m out of the required total of pounds 200m.
John Garside, the bid spokesman, says Bradford is "at the crossroads of the country," equidistant between Edinburgh and London.
Location is also a key issue for Birmingham, who propose to build a stadium just the other side of the M42 from the National Exhibition Centre. "We are very easy to get to from every part of the country," Alan Wenban Smith, an assistant director with Birmingham City Council, said. "If you are going to have a national stadium, there is a lot to be said for having it in the middle of the country."
Sheffield also claim a central geographical role - "situated in the centre of the country" - and have offered a possible late variation on extending the Don Valley stadium which currently holds 25,000 people, proposing an additional 80,000-seater stadium alongside to host football and rugby matches.
Whatever the group's decision, however, the rejected parties need not trudge away without hope.
"We do not rule out a future for other projects which do not achieve the national stadium bid," the Sports Council spokesman said. "There is Lottery money for other things as well."
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