The government would be in a "strong" legal position if the two-year Article 50 talks ended with no deal, the Lords EU Financial Affairs Committee said, BBC reported.
But it warned failure to reach any kind of financial terms would undermine PM Theresa May's aim of securing continued favorable access to EU markets.
It has been reported the EU may demand a "divorce bill" of up to £52billion.
May has warned the EU against punishing the UK for voting to leave in last year's referendum but several EU leaders have said the UK cannot enjoy better arrangements outside the EU than it currently has.
The peers, led by the LibDem peer Baroness Falkner of Margravine, said some member states could take legal action against the UK for any outstanding liabilities but it was "questionable" whether any international court could have jurisdiction.
"Even though we consider that the UK will not be legally obliged to pay into the EU budget after Brexit, the issue will be a prominent factor in withdrawal negotiations.
"The government will have to set the financial and political costs of making such payments against potential gains from other elements of the negotiations."
During their inquiry, the committee was told the UK had signed up to "concrete" commitments under the terms of the Multi-Annual Financial Framework, which sets a ceiling for EU spending up to 2020.
Professor Takis Tridimas, from Kings College London, said he believed these were legally binding under existing EU treaties.
But he said they could be amended in "unforeseeable circumstances", if all member states agreed, and that the Brexit vote would constitute such a circumstance.