Brexit Secretary David Davis said Britain intends to remain 'a European citizen'
He said Britain was looking for the broadest possible free trade deal with the EU and would seek cooperation on justice and crime policy that was as close as possible to today's arrangements.
Tacitly acknowledging the Baltic state's fear of Russian aggression, he also forecast Britain would continue playing "a large part" in maintaining Europe's security.
Speaking in Tallinn after talks with Estonia's chief Brexit negotiator Matti Maasikas, Mr Davis said: "When we leave the EU we both for altruistic reasons, but also selfish reasons, want the EU to continue to be a success.
"We want to see it prosper economically and politically, we want to see it be a strong force in world affairs in these days of various sources of instability over the world.
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Mr Davis said Britain was looking for the broadest possible free trade deal with the EU
"It is to our advantage in the UK to have a strong, stable and effective neighbour in the form of the union, so everything we do will be aimed at that, as well as of course our own interests too."
When we leave the EU we both for altruistic reasons, but also selfish reasons
As the House of Lords began their debate on the legislation to let Theresa May trigger formal talks with the EU, Mr Davis said he was "confident" her deadline of March 31 to invoke Article 50 of the Lisbon Treaty would be met, although he could not give a specific date.
On justice and home affairs, he said that "although we have issues about the European court's jurisdiction, we see that we can maintain the same sort of relationship that we currently have – we can try and get as close as we can to where we are today.
He was speaking after talks with Estonia's Brexit negotiator Matti Maasikas
He said: "On the issue of the single market, clearly we can't be in the single market… but we want to have the most comprehensive free trade agreement possible and we want to have a customs agreement to go with it. That we think is in everyone's advantage.
"Britain is a market for £290billion a year of European exports. Those are very important to Europe, just as our trade with Europe is important to us and we want to maintain that.
"But most important of all… we want to see a constructive negotiation leading to a long-term constructive partnership."
Stressing hopes that Britain and Estonia would continue to be allies after Brexit, he added: "Although we are leaving the EU we entirely intend and expect to continue to be a good European citizen, a good global citizen.
"We have long taken a strong stance on matters of defence and security, justice, home affairs, counter terrorism, all of these matters where we have played a large part in Europe's safety and stability, and we continue to expect to do so.
Theresa May wants to trigger Article 50 by the end of March
"So the departure from the union does not mean we expect to undermine that at all."
He spoke after reports that MEPs from other countries think Britain is trying to divide the EU ahead of formal Brexit talks, by targeting a charm offensive at potential allies among its smaller members.
It was also claimed on Sunday that some ministers want to divert some overseas aid cash to supporting eastern European countries in hopes of winning their backing for a good trade deal.