The Prime Minister held a series of private number-crunching meetings as chairman Herman Van Rompuy put back the start time in a bid to find a deal with a chance of agreement.
Summit officials said the talks were due to get underway five hours later than scheduled.
Mr Van Rompuy was due to table figures for a new budget compromise, after taking soundings with the waiting leaders.
One early pre-summit gathering involved David Cameron, German Chancellor Angela Merkel, Mr Van Rompuy and European Commission President Jose Manuel Barroso. But French President Francois Hollande, also due to take part, let it be known after the meeting had started he could not make it.
Last night, Mr Cameron separately exchanged budget chat with his Dutch, Swedish and Danish counterparts, as other leaders also broke off into groups – roughly splitting along north-south lines – the northern EU countries being most keen on deep EU budget cuts, and the southern member states, who benefit most from budget handouts, less keen.
Exact figures were kept private, with Belgian Prime Minster Elio Di Rupo resorting to Twitter to suggest, whatever the numbers were, they remained “unbalanced”. Commission officials pointed out that cuts had already been made in the original budget proposal and the current figure on the table already amounted to a reduction in spending compared with the current seven-year budget period.
Allowing for current exchange rates, the opening bid on the table amounts to a budget proposal of 913bn euro (£778bn) for 2014 to 2020. British Government sources said Mr Cameron wanted to see a further cut of “ten of billions” off that figure.
One Commission official acknowledged that, in place of the 913bn euro figure the UK delegation “would like to see a number with an eight at the front”. In sterling that would mean a maximum acceptable figure of £766.6bn.
Mr Cameron set out his stall as soon as he arrived at the summit venue earlier, saying: “The numbers are much too high.
“They need to come down – and if they don’t come down there won’t be a deal. The European Union should not be immune to the sorts of pressure we have to reduce spending, find efficiencies and spend wisely – what we are all doing.”