One major milestone in London that cleared the way for Chinese banks came in 2013, when all foreign banks were allowed to open branches in the city. By opening branches, ICBC and CCB have had greater opportunities to offer its services than they would have if only allowed subsidiary status.

Branches, seen as overseas arms of international banks, have lending and financing capacity proportionate to the parent company's balance sheets. Subsidiaries, in contrast, are subject to the strict capital requirements that apply to local banks in the United Kingdom. In most cases, the lending and financing capacity is proportionate to the balance sheets of the subsidiary itself.

Andrew Carmichael, a partner at Linklaters law firm in London, said having a full branch license makes it much easier for a Chinese bank to offer funding to British, and to some degree, all European Union borrowers. The regulatory easing dovetails with the significant amount of trade with China, an increasing proportion of which will be settled in the Chinese currency, he adds.

Carmichael said it is also important for Chinese banks to internationalize because their customers may use yuan for acquisition financing but will need local funding for ongoing operations.

He says his team at the law firm is already seeing State-owned enterprises and other Chinese organizations issue euro-denominated bonds, which gives businesses local funds and banks the ability to lend in local funds.

What's more, European financial markets not only offer Chinese banks a chance to internationalize but also teach them how to learn to be a player in the global financial system.

"London is the foreign exchange and capital market center and to a major degree the loans center for Europe. Other cities give local openness, which may be significant. Luxembourg, for example, is the fund center," Carmichael said.

Chris Cummings, chief executive of TheCityUK, said his team is looking to help grow the two nations' existing relationship in financial services and related professional services. "Chinese banks could be significantly more active in London and, as China is a major economy and the world's largest exporter of goods, we believe that there is huge scope to increase Chinese banks' presence in London."

Huo Rongrong, head of China and renminbi business development at HSBC Europe, the Middle East and Africa, said: "Chinese banks are an important force in the internationalization of the renminbi. Their unparalleled experience and extensive knowledge in China's onshore market warrants their natural transition into the offshore renminbi market."

Huo said HSBC's global expertise complements the Chinese banks' push for the internationalization of the renminbi.

Evan Goldstein, Deutsche Bank AG global head of renminbi services, said that the role of Chinese banks as clearing agents in Europe has helped to increase the awareness of major corporations in the use of the yuan as a trade settlement currency.

"The Chinese banks are valued members of the city of London's working group on renminbi internationalization. They have a unique perspective on business flows and transaction volumes in their capacity as offshore clearing banks in the major centers," he said.