Brexit Secretary David Davis returns to Brussels on Thursday to conclude the second set of four-day talks with EU negotiators with hopes of making progress on how the so-called "divorce bill" is calculated.

The payment made by Britain to settle outstanding liabilities, which could run to tens of billions of pounds, has emerged as a key battleground in Brexit talks.

Both sides are hoping to reach agreement on the method of calculating the financial settlement by October's European Council summit.

The negotiations have so far focused on so-called "phase one" issues of separation - including the financial settlement, citizens' rights, the Irish border and Britain's position in relation to Europe's civil nuclear regulator, Euratom.

European Commission chief Brexit negotiator Michel Barnier is keen to make progress on the divorce bill settlement so he can recommend to EU leaders that "phase two" negotiations can begin on Britain's future trading relationship with Brussels.

Mr Davis is expected to hold a press conference alongside Mr Barnier, although it has not been confirmed by either side.

Earlier this week, the European Commission dismissed criticism of David Davis for leaving Brexit talks after an hour-long meeting with Mr Barnier.

The Brexit Secretary was rounded on by opposition parties for leaving the four-day talks on Monday and for being photographed without any papers at the meeting, while Mr Barnier and his team had stacks of notes in front of them on the table.

The photograph led to claims Britain was unprepared for the talks amid a damaging Cabinet row apparently over the shape of Brexit at home.