Barry Cleverdon, the chief executive of the National Exhibition Centre group, which includes the ICC, says he believes the proposal should not proceed and that there is insufficient demand to support both.
"The International Convention Centre in Birmingham is regarded as a world centre," says Mr Cleverdon. "It serves this country very well, attracting a wide range of important conferences into this country, particularly those with 8,000 to 10,000 delegates at a time, who will use the local tourism facilities as well.
"London already has a convention centre [at Westminster] meeting the needs of the capital. If [King's Cross] does go ahead it will enter a market we have been in for some time, and will be another competitor in the way we compete with Paris, Milan and Singapore.
"This facility in Birmingham was funded by the city of Birmingham, and continues to be so. ICC delegates spend money here. A survey two-and-a- half years ago found that more than pounds 110m a year spending in the local economy was generated by the ICC conference programme. It is a very important factor.
"My personal view is that it would be unfair for lottery funding to be used [for King's Cross] because we already have a facility serving us so well."
This opinion is backed by Birmingham City Council, which is to ask the Government to rule out lottery money going to a King's Cross convention centre. Carl Rice, chair of Birmingham's NEC-/ICC committee, says: "I don't know which lottery fund they would apply to. They would need a rigorous business plan, and I can't see how they can have a business plan that will stack up.
"None in the world break even, they are all loss leaders to stimulate the local economy, so it will be interesting to know which backers are putting money up to absorb a loss.
"Any logical person will oppose it, and we will do so. We will point out the incompatibility of it alongside Birmingham's. It would be a great folly to use public money for it. It is an absurd proposal. Increasingly the convention business is being dogged by over-capacity.
"There has been a pounds 150m investment in a state-of-the-art facility in Birmingham, backed by European money. It is one of the best in Europe, and it would be more appropriate for London to focus on something where there is less competition. They should get their own facilities that don't compete with others. Only one major facility is appropriate in the UK."
The Greenwich Millennium Experience is more relaxed about the King's Cross proposal. Although it has been reported that the Greenwich dome is to become a business exhibition centre after the year 2000, this is denied by the company that now runs the development. A spokesman for the Millennium Experience Company said that a planning application has been submitted for the long-term use of the dome as a sports stadium and leisure and entertainment complex, and that a business convention centre will form no part of the development.
London's Chamber of Commerce, which is heading the King's Cross plans, is not put off by the criticisms from Birmingham. Andrew Hawkins, director of policy at the chamber, says the development would be viable.
"We want to attract major pharmaceutical conferences and conventions," says Mr Hawkins. "The science community is a good example of why we need big events, and announcements of big scientific discoveries to promote London's image of research."
If a 10,000-seat convention centre is built at King's Cross it will use a disused grain warehouse next to the rail station, which is to become a major international arrival and departure point. The proposal is backed by the owners of the site, London & Continental Railways, the National Freight Corporation and British Waterways, as well as the Confederation of British Industry and other potential users, including the British Medical Association and the Council of Science and Technology Institutes. A meeting last week of the King's Cross Partnership confirmed the go-ahead for the project, and decided to set up a steering group to oversee the development.