The sweeping new national security law that Beijing imposed on Hong Kong in June is one major trouble spot. The U.K. says the law violates an agreement China and Britain signed in 1997, when the U.K. passed sovereignty of Hong Kong, its former colony, to China. In response to the law, the U.K. extended British citizenship rights to some Hong Kong residents in July, a move that Beijing condemned as foreign interference in domestic affairs.

Another point of tension is the U.K.'s treatment of Chinese telecommunications giant Huawei Technologies. The U.K. announced in July that British telecoms providers will be banned from using Huawei equipment in the U.K.'s 5G mobile network, citing national security risks. (Huawei has previously denied allegations that its products pose security risks.)

That was the state of play when Caroline Wilson, a diplomat with previous posts in Beijing, Brussels, Moscow, and Hong Kong, was tapped to become British Ambassador to China in June; and she formally assumed the role in October.

"It's a difficult time and I sometimes have to manage differences and controversial, sensitive aspects of the relationship," Wilson said in an interview at Fortune China's Most Powerful Women Summit in Shanghai on Thursday. "We're not always going to be able to agree on everything, but basically there's so much that we have to do together."

Wilson identified public health and climate change as two vital issues she plans to address in her role as ambassador. She said China can "do more" to ensure the world's poorest countries have access to COVID-19 vaccines.

On the vaccine front, "China does a huge amount globally," Wilson said, citing China's participation in COVAX, a global initiative to ensure equitable access to coronavirus vaccines. "But we think they could do even more and be even more effective," she said.

Climate change is another area where she hopes the U.K. and China can pool their efforts, Wilson said.

In November, she visited China's southern metropolis of Shenzhen to advocate for more climate change collaboration between the U.K. and China through projects like a joint tech lab for offshore wind.

"Showing that we can get global action on climate change is going to be very important," Wilson said, pointing out that both countries are scheduled to host major environmental summits in 2021—the UN biodiversity conference in Kunming, China, in May, and the UN Climate Change Conference, also known as COP26, in Glasgow in November.

Chinese President Xi Jinping's September announcement that China will aim to reach net-zero carbon emissions by 2060 and peak carbon emissions by 2030, Wilson added, "is very, very significant" for global climate goals.

In laying out her top priorities, Wilson said the coronavirus pandemic has shown that countries need to work together on global issues like public health and the environment "more than ever."

"I want to build a strong relationship between the U.K. and China. To do that, I want to show that this is a relationship that delivers, both for people in China and for people in the United Kingdom," Wilson said.

Still, she acknowledged that the rocky period in the U.K.-China relationship called for "frank dialogue...to allow for management of differences and divergence of view."

And Wilson, a fluent Mandarin speaker who flitted between English and Chinese while answering audience questions, says she's well-suited for the challenge.

"At the present time, the personality of the ambassador is quite important," she said. This moment in history calls for "the human touch—showing that we are all human and that we have more interests in common than [what] divide us," she said.