Experts in Britain spoke highly of his proposal and expressed confidence in bilateral relations in the future.
Martin Jacques, a senior fellow at the Department of Politics and International Studies, Cambridge University, told Xinhua that with Britain facing the enormous challenge of Brexit, May attached great importance to her visit to China to strengthen bilateral cooperation, especially in economy and trade, which is an indispensable step to push forward her "Global Britain" plan.
He said Xi's proposal to forge an enhanced version of the "Golden Era" of bilateral ties not only shows that China will maintain its opening-up policies and cooperation with Britain, but will also help consolidate the achievements of China-Britain relations in recent years.
He especially appreciated Xi's proposal that both countries should enhance exchange and cooperation within multilateral institutions such as the United Nations, G20 and the World Trade Organization to address global challenges, including climate change.
China and Britain could jointly put forward more proposals in multilateral institutions, which is "a natural following step" after the deepening of their relations, he said.
Fu Xiaolan, professor of Technology and International Development at the University of Oxford, said the bilateral cooperation will have vitality only if it is practical and involves specific fields.
"The two countries face common global challenges including climate change, trade protection, anti-terrorism, poverty reduction and food safety. China and Britain have much room of cooperation (on) these global issues," Fu said.
Both sides can get strength from each other and exert great influence on the global stage, she added.
Keith Bennett, deputy chair of the 48 Group Club, a consultancy network for British companies seeking to do business with China, said Britain is at a crossroads as Brexit looms and there is still no roadmap for the way ahead.
"At this crucial time ... it is only China that is putting forward a clear, strategic line for our future bilateral relations, based on equality and mutual benefit," he said.
Bennett said Britain used to be a key gateway to Europe for China. China and Britain can be closer partners as their economies are highly complementary.
By combining their respective strengths, they have much to contribute to third-country markets, particularly in Africa, as well as in countries such as Pakistan and in Central Asia, he said.
"The key context for this is the Belt and Road Initiative (BRI) put forward by President Xi Jinping. Britain showed great foresight in becoming the first G7 country to sign up to the Asian Infrastructure Investment Bank. The same foresight is now needed with regard to BRI," he said.
Bennett also said China and Britain are both leading powers in innovation and should explore together such fields as artificial intelligence and big data, not only from the technological point of view but also in terms of establishing ethical and regulatory frameworks.
"The British government is also facing strong countervailing pressures from across the Atlantic, whilst grappling with the unprecedented challenge of Brexit. It is hoped that Britain can make a wise and strategic choice and grasp the hand extended by China," he said.
Anthony Glees, director at Centre for Security and Intelligence Studies at the University of Buckingham, told Xinhua observers welcome the cordial way in which May and her entourage were received in China, and regard as hugely significant Xi's positive and encouraging words to Britain, given the current uncertainty and turmoil.
China has come to be seen not just as an economic partner for many Western states but also as a long-standing supporter for stability in the Asia-Pacific, and a doughty opponent of those who try to change the status quo with violence, he said.
However, Glees added that to forge the much-desired enhanced "Golden Era", a great deal of work will have to be done. In almost all economic fields, apart from road vehicles, Britain needs to export far more to China than the current export volume once it is out of the EU to up its game.
He said over the years Britain has learned to value Chinese imports. The amazing growth of the Chinese economy and the rapid expansion of its network of new cities, many with populations of over one million, mean British goods and services, including high-level education, must make substantial strides for Britain to reap the benefits.
Glees said the proposals made by Xi during May's visit will certainly be seized upon in Britain by those prepared to devote efforts to understanding the demands of the Chinese marketplace and how Britain can meet them.
"We in Britain need to understand that China's most important partner in Europe will continue to be the European Union. And once we have come to agree (on) terms on our relationship with the EU27, which China was keen to see, new opportunities could well emerge," he said.
Since assuming office in 2016, May kicked off her first official visit to China last Wednesday. During her visit the two countries signed a dozens of deals in areas including trade, finance, healthcare and smart cities.