But the deal masks a fudge over the wording of a statement to be issued today by the Government, which may yet dog the organisers of the pounds 580m scheme featuring a massive dome at Greenwich.
Following the intervention of Tony Blair at the express request of the deputy prime minister, Michael Heseltine, the two parties agreed to sign the statement.
But Labour claimed last night that the safeguards on overspending it had sought were included. Labour's support for the project was vital to ensure that private sector sponsors, expected to contribute up to pounds 150m, would put in money.
Labour had held out on three issues, seeking a cap on the overall budget, a limit on contingencies and the right to review the project if elected.
In particular, Labour sought to ensure the overall budget would be pounds 580m and that the extra pounds 195m for contingencies would only be used as a last resort. The Millennium Commission is already contributing pounds 200m to the scheme and Labour wanted to ensure no more Lottery money was spent.
Yesterday Labour sources were claiming victory on all three points after discussions with the Government, saying they had a guarantee that the contingency budget would only be used in an emergency.
This then caused difficulties for the Millennium Commissioners who did not want to put in their pounds 200m without the expectation that some of the contingency fund would be used. However, late last night, Commission sources said that the wording of the parties' joint statement was acceptable for the future of the Exhibition.
The intervention of Mr Blair proved crucial as he was determined to ensure that Labour was not blamed for the collapse of the Exhibition.
However, moves towards a consensus were not helped when John Major launched an attack on Labour's attitude to the Millennium Exhibition on BBC local radio: "The Labour party have had their representative on the discussions and debate over this project from the outset," he said.
"They can't claim not to have known what the situation was. It's very surprising at the last moment that they have failed to understand what is going on and created this difficulty."
While the Exhibition has now got over its first hurdle and the pounds 20m purchase of the land will be able to go ahead, one source close to the negotiations said: "This is unlikely to be the last crisis over this Exhibition."
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