The UK government wants China to pay for a number of "northern powerhouse" projects as well as backing deals in Britain's creative and technology industries.
British officials and business leaders say the rise of China is impossible to ignore: China's economy is four times the size of Britain's.
Cameron wants to make London, the biggest global foreign exchange center, into the dominant Western hub for trading, clearing and settlement of renminbi.
The opening (of a conference of UK Confucius institutes) was also attended by Prince Andrew, the Duke of York, who said: "I'm very proud of the fact that I'm sometimes considered one of the long-term friends of China". He said he regretted having learned only French at school because "when you learn another language you become worth two people".
At the pub, Mr Cameron told Mr Xi the "famous" story of how in 2012 he drove off from the pub near Chequers without his daughter Nancy, then aged eight. Speaking while drinking a pint of ale with Mr Xi, he said: "I once famously made a terrible mistake. I got into the car and I left my daughter.
"I've been in here a few times but I'm not leaving my family here today. She (Nancy) tells the story about her dad in the pub. She's coped very well."
On Friday, during a trip to Manchester to hear about the UK's plans to revive northern cities by creating a "northern powerhouse", Xi will visit Etihad stadium, home of Manchester City.
British officials are hoping to boost football's prospects in the world's most populous nation.