When Britain leaves the European Union at midnight on Friday the bloc loses the second-biggest net contributor to its budget, leaving a 12-billion-euro ($13-billion)

hole in its finances.

The United Kingdom will continue making budget contributions this year under an agreed post-Brexit transition period. But from 2021 Europe will have to look elsewhere.

This further complicates an already fraught debate between the remaining member states over the EU's 2021-2027 long-term budget, called the Multiannual Financial Framework (MFF).

But a so-called "Frugal Five" of wealthy mainly northern countries -- Austria, Denmark, Germany, the Netherlands and Sweden -- are seeking to limit EU expenditure.

And a rival "Friends of Cohesion" group of 16 eastern and Mediterranean countries wants to defend the budget rules.

Charles Michel, president of the European Council which represents member state governments, has called an MFF summit that will "begin" on February 20 and likely drag on.

- Farm subsidies under pressure -

According to European Commission estimates, Britain's net contribution -- the amount it pays in less EU spending on UK projects -- would have been 12 billion euros a year.

Over the period of the upcoming seven-year MFF that leaves an 84-billion-euro shortfall in the Commission's financial plans.

The previous finance commissioner, Gunther Oettinger, wanted to fill the gap by increasing member state contributions and cutting traditional big spends: cohesion and farm subsidies.

This would allow Europe to switch funds to more "modern" areas, like investing in green technologies, coping with migration and moving into the defence field.

But much of this is very sensitive in EU capitals, and Michel has trekked all over the continent for talks without much sign of a breakthrough.

"We might have hoped that Brexit would be a shock to the system, but I think we'll just go on as before," laments Nicolas-Jean Brehon, of the Robert Schuman Foundation.

Some of the richest members of the union want to limit contributions to only one percent of each member state's GDP.

"It's obviously a symbolic threshold. It's also a political threshold that Germany and the British were insisting on," Brehon told AFP, noting that Brexit cost Berlin an ally.

- Big spenders -

The European Commission, meanwhile, wants to set the level at 1.114 percent of EU GDP, which would imply a 1.134-trillion-euro budget at 2018 prices, or 1.279 trillion at current levels.

The European Parliament would like an even higher 1.3 percent.

Taking into account the British departure, the current multiannual budget represents 1.16 percent of European Union GDP.

Another Commission idea is phasing out the "rebates" that late British premier Margaret Thatcher famously demanded, taken up by some of the other bigger spenders.

After Brexit these reductions in budget contributions will only apply to Austria, Denmark, Germany, the Netherlands and Sweden -- perhaps not un-coincidentally, the Frugal Five.

For the Commission and the countries that are net recipients of EU funds, it is wrong that -- thanks to these rebates -- the frugals spend less in percentage terms of their per capita GDP.

But Germany, for one, has noted that even if spending is reduced and capped at one percent as it demands, it will still end up paying more after Brexit.

The debate will continue and has given new impetus to calls for the European Union to develop its own revenue streams, perhaps by a tax on plastics or on EU carbon trading.afp