"We have seen real progress and I'm committed to maintaining that positive trajectory," James Cleverly said in the European Parliament, as he co-chaired a joint committee on cross-Channel relations with European Vice President Maros Sefcovic.
British Prime Minister Rishi Sunak has sent Cleverly and, last week, his finance minister, Jeremy Hunt, to Brussels to reinforce relations following the Windsor Framework deal he struck with the EU in March.
That pact put to bed a dispute over post-Brexit trading arrangements for Northern Ireland, the British territory that shares a border with Ireland, with the aim of unlocking UK access to EU programmes.
The successive visits also came as the British public increasingly views Brexit as a mistake, with nearly half expressing a wish to rejoin the European Union in the future, according to a British YouGov survey released last week.
"We have to recognise that we will not agree on everything. But in mature relationships, we can deal with differences, whilst making the most of the areas where we agree," Cleverly told the joint committee, the EU-UK Parliamentary Partnership Assembly.
The British minister underlined close cooperation London and Brussels are showing in supporting Ukraine militarily and financially as it faces down Russia.
Cleverly was also to visit NATO headquarters in Brussels, where he was to speak with alliance chief Jens Stoltenberg ahead of a summit of allies in Lithuania next week.
Cleverly was to voice London's backing for Sweden to become a NATO ally "as soon as possible," according to a British foreign office statement.