European Commission President Jean-Claude Juncker has warned the UK it faces a "very hefty" bill for Brexit.
He promised two years of "tough negotiation", when discussions on leaving terms get under way between the government and the European Union.
Exit will not come "at a discount or at zero cost", he said in a speech to the Belgian Federal Parliament.
Reports suggest the UK could have to pay the EU up to 60 billion euros (£51bn) after Brexit talks start.
Mr Juncker's comments came as the House of Lords held a second day of discussion of the government's European Union (Notification of Withdrawal) Bill, which, if passed into law, will allow Prime Minister Theresa May to trigger Article 50 of the Lisbon Treaty, allowing formal talks with the EU to start.
She is hoping to do this before the end of March, with EU negotiations expected to take up to two years.
Discussions are taking place in Brussels on the size of the bill to be presented to Mrs May when she launches the talks. The amount will cover the UK's share of the cost of projects and programmes it signed up to as a member, as well as pensions for EU officials.
In his speech, Mr Juncker, a former prime minister of Luxembourg, said: "It will be a tough negotiation which will take two years to agree on the exit terms. And to agree on the future architecture of relations between the United Kingdom and the European Union we will need years.
"The British people have to know, they know already, that it will not be at a discount or at zero cost. The British must respect commitments they were involved in making. So the bill will be, to put it a bit crudely, very hefty."
How Brexit will work
Unpicking 43 years of treaties and agreements covering thousands of different subjects was never going to be a straightforward task.
It is further complicated by the fact that it has never been done before and negotiators will, to some extent, be making it up as they go along.
The post-Brexit trade deal is likely to be the most complex part of the negotiation because it needs the unanimous approval of more than 30 national and regional parliaments across Europe, some of whom may want to hold referendums.
He added: "We need to settle our affairs not with our hearts full of a feeling of hostility, but with the knowledge that the continent owes a lot to the UK. Without Churchill, we would not be here - we mustn't forget that, but we mustn't be naive.
"Our British friends will need to understand that we want to continue to develop European integration."
But an ally of German Chancellor Angela Merkel said it was "not very smart" of the European Commission to ram home the cost of Brexit at this stage.
Stephan Mayer, a CDU member of the German Parliament, told the BBC that while Brexit would be "expensive for both the UK and the EU", much would depend on which EU programmes the UK continued to participate in.
"I am not so happy with this aggressive line," he told BBC Radio 4's Today.
"I am convinced that Germany has a special interest in stable and good relationships with the UK. I fear in a certain way that this harsh pressure, which is put by the European Commission on the UK, is not in Germany's interests."
Mrs May has already said the UK will leave the European single market, but has promised to push for the "freest possible trade" with European countries.
In a speech in January outlining her priorities for Brexit, she warned the EU that to "punish" the UK for leaving would be "an act of calamitous self-harm".
Earlier this month, the House of Commons overwhelmingly backed the EU Bill and the government has said the Lords must not "frustrate" its passage into law.