LONDON — The U.K. government has proposed extending the next round of Brexit negotiations on a rolling week-by-week basis until a breakthrough is reached on the contentious issue of Britain's "exit bill," according to two U.K. officials familiar with the proposal.

A "very senior" member of Britain's negotiating team explored the possibility of "continuous negotiations" during talks with an EU counterpart over the last few days, the officials said. The move would see British negotiators camped in Brussels semi-permanently in a bid to break the deadlock over Britain's financial obligations to the EU.

It comes amid mounting concerns on both sides of the Channel that there is not enough negotiating time left before the next European Council meeting in October, when EU leaders will decide whether "sufficient progress" has been made in order for talks on a future trade deal to begin.

The U.K.’s initiative comes as London gears up for an intensive two-week push to prepare the way for Britain’s eventual exit in 2019, with a flurry of new position papers and the publication of three core elements of the government's Brexit legislative program.

Four new position papers setting out the U.K. government's negotiation proposals in key areas affected by Brexit have been pencilled in for publication before parliament breaks for recess on September 15, according to the two U.K. government officials who spoke to POLITICO separately.

The four papers will cover "internal security," "external security," “fair and open” trade — which explores options for mutual regulatory standards with the EU — and “science and innovation." The science paper is expected to be published on Wednesday. A fifth position paper, which could be signed off in time to be published before the break, covers the future of Britain’s service sector economy.

On top of the position papers, the government intends to publish three draft Brexit bills — in the form of government white papers — in the coming weeks, ideally before parliament goes off for recess the week after next, the two officials confirmed separately. The bills will be on customs, immigration and trade, according to the officials, who spoke on condition of anonymity.

The bills are necessary to smooth Britain's eventual exit from the EU, setting out how the border checks will work. They come on top of the Repeal Bill, now known as the EU (Withdrawal) Bill, which returns to the Commons on Thursday for a two-day debate before MPs vote on Monday.

One Whitehall official told POLITICO the white papers were more significant than the position papers and represented the first concrete steps to a future outside the European Union.

White papers are the first stage in the U.K. legislative process and as such, their publication signifies the formal first stop on the road to a policy becoming U.K. law. The white papers on customs, immigration and trade will all affect the parameters of what is achievable in the Brexit negotiations, more so than the "position papers," which can be easily amended, or thrown away entirely, should the negotiations with Brussels offer up alternative solutions.

The flurry of government activity over the next two weeks exposes a growing determination in London to speed up the Brexit process after an extended period in which little progress was made due to June's general election and continuing cabinet splits over the best route out of the EU. It also reveals the government's determination to show that it is in charge and determined to get on with the job, amid mutterings in Westminster over Prime Minister Theresa May's future.

The British proposal to extend the negotiations envisages the next round of talks, due to start on September 18, being extended indefinitely, with U.K. officials returning to Brussels week after week until a breakthrough has been reached on the financial settlement.

The move is indicative of concern in Westminster that time is running out to make enough progress on the divorce settlement to be able to move on to Britain’s principal strategic negotiating goals: agreeing a transitional arrangement upon Britain's departure and a longer-term “deep and comprehensive” free-trade agreement. Appearing on the Andrew Marr Show Sunday, Brexit Secretary David Davis accused the EU of trying to use the looming deadline as leverage in the negotiations. "They are trying to play time against money," he said.

Agreement has not yet been reached for the September talks to be extended indefinitely, but U.K. officials appear confident Brussels can be persuaded. Both sides have acknowledged that the pace of talks may need to be intensified. “Time is passing very quickly, and if required, we are ready on our side — the 27 EU member states and the European institutions — to step up the pace of negotiations,” EU chief negotiator Michel Barnier said at the closing press conference following last week’s talks.

But on Sunday, the European Commission was skeptical of the merits of the U.K. proposal, insisting that while Brussels was open to additional rounds of negotiations, merely more time to talk in itself isn't enough. "We have said since July that we are ready to add negotiation rounds, but we need substance from the U.K. to further discussions and to be able to make progress," one official said.

Papers prepared

The immediate obstacle to progress in the Brexit talks is the question of Britain’s ongoing financial obligations after leaving in 2019. Unless EU leaders determine “sufficient progress” has been made on the money and other withdrawal issues, Brussels will not move to the next stage of talks on the future EU-U.K. trading relationship.

European Union leaders, including May, are due to meet in Brussels on October 19-20, when they will review the state of the talks so far.

If EU leaders refuse to allow talks to progress, negotiations over future relations will likely not be able to begin until the next European Council in December, which would leave less than year in which to negotiate an agreement, assuming talks must be completed by October 2018, to allow the EU and national parliaments time to ratify the deal.

The exit bill is one of three key issues — along with the Northern Irish border and citizens’ rights — which the EU wants to see progress on before talks can proceed to the next stage. While some progress has been made on the border and citizens' rights, as well on a broad set of technical matters that negotiators call “separation issues,” the bill is proving problematic.

According to officials familiar with the negotiations, the Commission wants to treat all of the U.K.’s obligations under the EU’s seven-year, 2014-2020 financial framework as a starting point. The U.K., in contrast, wants to go through each obligation line by line. Fundamentally, the EU wants Britain to prove why it does not owe money. The U.K. wants Brussels to prove why it does.

In Brussels, there is widespread irritation with the British for seeking to dictate the terms of their departure, which the rest of the EU did not ask for, nor desire. If Britain wants a trade deal with the EU, so the argument goes, then it needs to play by the rules of the game set in Brussels, not London.

In Westminster, the EU’s position is seen as unnecessarily intransigent and founded on a wish to punish the U.K. rather than arrive at an equitable and legally sound agreement. Liam Fox, the international trade secretary, has accused Brussels of trying to “blackmail” Britain.

Bill battle

EU officials say the final cost to the U.K. could amount to around £59 billion (€65 billion), an estimate largely based on Britain’s current share of the EU’s common budget, or around 12.5 percent, through to 2020, the final year of the bloc’s current long-term budget that the U.K. approved. Neither side has officially put out its own estimate, and such is the political sensitivity in London that it's even refusing to set out its approach in a position paper.

Two U.K. newspapers on Sunday reported that May is prepared to pay up to £50 billion over three years after Brexit, although Davis flatly denied the claim on the BBC.

Both sides originally agreed to hold one week of formal negotiations per month, but the last round of talks broke up after barely 48 hours, having begun on Tuesday at 11:30 a.m. and ending Thursday before noon. The haste with which the talks broke up was also widely seen as indicative of the lack of consensus between the two sides.

The last round of talks in Brussels ended in barely concealed acrimony, with Barnier accusing Britain of refusing to acknowledge its financial obligations.

Speaking in the U.S. on Friday, Davis acknowledged the looming deadline, telling reporters the EU-U.K. divorce negotiations were the “most complicated negotiation in history,” adding: “Our enemy in a way is time.”

David M. Herszenhorn contributed reporting.