The Chinese leader, Xi Jinping, has said the UK’s relationship with his country had gone through “twists and turns” over the years but that a more “consistent” approach was in both their interests.

Ahead of talks with Keir Starmer during the first visit to China by a British prime minister in eight years, Xi said the two men would “stand the test of history” if they could “rise above differences”.

In the Great Hall of the People in Beijing, Xi also appeared to reprimand Kemi Badenoch, the Conservative leader, who has criticised Starmer for travelling to China this week.

There has been cross-party concern about China’s spying activities in the UK – with the travelling No 10 delegation operating on burner phones – and also Beijing’s human rights abuses.

However, the UK prime minister began the trip by saying he wanted to bring “stability and clarity” to the bilateral relations after years of “inconsistency” under the Tories when it went from “golden age to ice age”.

After their meeting, Starmer said the relationship between the two countries was now in a “good, strong place” after “productive” talks, and made a series of announcements that could unlock new opportunities for British businesses.

In a significant move, China agreed to a visa waiver for British tourists and business travellers, ending the requirement for travel to be no more than 30 days and bringing the UK into line with 50 other countries.

The UK also signed a series of agreements with China on closer economic cooperation, including greater trade and services, making it easier for British firms to operate there including a $15bn (£10.8bn) investment by the pharmaceutical firm AstraZeneca in its Chinese operation.

Downing Street said the meeting was “constructive” on a number of issues, including the fate of the jailed Hong Kong pro-democracy activist Jimmy Lai – whose release the UK has urged – and the lifting of sanctions on British MPs and peers.

The leaders discussed the Ukraine conflict, and were “quite clear they have the same goal” of ending the war, with peace talks playing a part. But No 10 would not say whether Starmer – who spoke to Volodymyr Zelenskyy on the eve of his visit – pressed Xi to try to restrain Russia.

With Starmer under pressure at home not to sacrifice national security for the sake of closer economic ties with the world’s second biggest economy, Downing Street confirmed that security was discussed more broadly. It said there were “constructive” discussions on rebuilding the UK embassy in Beijing.

In opening remarks before their talks, Xi had told Starmer: “Your visit this time has drawn a lot of attention. Sometimes good things take time. As long as it is the right thing that serves the fundamental interests of the country and the people, then as leaders we should not shy away from difficulties and we should press ahead.

“As long as we take a broad perspective, rise above differences and respect each other, then we will prove ourselves able to stand the test of history,” he added.

But Xi did acknowledge that the UK-China relationship had seen “twists and turns” over the years that he said served the interests of neither country.

Against a backdrop of Donald Trump’s ambitions for Greenland, tensions with Iran and Vladimir Putin’s war in Ukraine, Xi suggested that in such a turbulent world it was essential for the two countries to work together for “world peace”.

Describing the state of the world as “turbulent and fluid”, Xi said more dialogue between the UK and China was “imperative”, whether it was “for the sake of world peace and stability” or for both economies.

Starmer told Xi he wanted a “more sophisticated” relationship between the two countries. “It is with the British people in mind that I am here today. I made the promise 18 months ago when we were elected into government that I would make Britain face outwards again.

“Because as we all know, events abroad affect everything that happens back in our home countries, to prices on the supermarket shelves to how secure we feel.”

At the UK-China Business Council later, Starmer told delegates Xi had recounted a story about blind men being presented with an elephant. “One touches the leg and thinks it’s a pillow, another feels the belly and thinks it’s a wall,” he went on.

“And too often this reflects how China is seen. But I profoundly believe that broader and deeper engagement … is our way of seeing the whole elephant and therefore building a more sophisticated relationship fit for these times.”

Xi also praised former Labour governments, under Tony Blair and Gordon Brown, for working constructively on bilateral relations in the past.

The bilateral meeting ran to an hour and 20 minutes, almost double the allotted time, followed by private talks with Xi and his foreign minister along with Starmer and his national security adviser, Jonathan Powell, and then lunch in the ornate Golden Hall, where along with global affairs, they discussed Shakespeare and football.