* Trip is Li's first to UK since taking office
* UK's Cameron announces deals worth more than 14 bln pounds
* China keen to put rights row behind it
* Trade deals focus on energy, finance sectors
(Updates after news conference, add details of trade deals)
LONDON, June 17 (Reuters) - Britain and China signed deals on Tuesday worth more than 14 billion pounds ($23.5 billion) during a visit by Chinese Premier Li Keqiang, with energy and finance dominating the trade agenda.
In a trip aimed at deepening commercial ties between the world's second-largest economy and Europe's financial capital and drawing a line under a row over Tibet, Li met Queen Elizabeth and held talks with Prime Minister David Cameron.
Cameron said the rise of China was "one of the defining events of our century" and that Britain wanted to strengthen ties on every level, from business to cultural understanding.
"Today we have signed deals worth more than 14 billion pounds, securing jobs and long-term economic growth for the British and Chinese people," Cameron told a news conference.
Li, on his first official trip to Britain since taking office, said the two countries had extensive shared interests.
"China is ready to work with the UK to foster a partnership for growth and inclusive development to ensure that this relationship will grow faster and in a healthier way," he said.
SPATE OF DEALS
Oil major BP signed a 20-year deal worth around $20 billion to supply China National Offshore Oil Corporation (CNOOC) with liquefied natural gas (LNG) cargoes, BP Chief Executive Bob Dudley said at a conference in Moscow.
"It is a fair price for them and a fair price for us. It is a good bridge between the UK and China in terms of trade," Dudley said.
Shell also announced that it had signed an agreement with CNOOC strengthening its existing strategic ties.
And the London Stock Exchange said it had signed agreements with two of China's biggest banks to develop offshore trading in the Chinese currency, the yuan.
London, which dominates the $5-trillion-a-day global foreign exchange market, is seeking to fend off challenges to its position as the leading yuan centre in Europe.
Also on the table is a deal to make China Construction Bank (CCB), the country's second-largest lender, the first clearing service for offshore trading of the Chinese currency in London.
China views Britain, the world's sixth largest economy and home to the only financial capital to rival New York, as Europe's most open place to do business. Its firms are keen to invest in major nuclear and high-speed rail projects.
The state-owned China Development Bank Corporation (CDB), which finances government-led infrastructure projects and is looking to expand its overseas investments, signed a deal to build closer ties with TheCityUK, which represents Britain's financial industry.
Lloyds Banking Group also signed a memorandum of understanding with CDB to help secure inward investment from China, with a focus on energy and infrastructure.
China, whose $9 trillion economy is over three times the size of Britain's, wants to use the visit to put past differences with London over Tibet behind it.
Britain's relations with China took a nosedive in 2012 after Cameron met the Dalai Lama, the Tibetan spiritual leader who Beijing says is a separatist. Ties have recovered somewhat since, and Cameron visited China last year.
But tensions remain.
China has ruled Tibet since 1950, and Beijing warned London on the eve of Li's visit not to lecture it on the subject if it wanted good economic ties. British Deputy Prime Minister Nick Clegg said on Monday that the people of China were politically shackled to a Communist one-party state.
Asked about Clegg's comments, Li said that China's constitution required human rights to be respected, and that the country was choosing its own path on the issue.
"There are diverse dimensions to the issue of human rights, and countries which are at different stages of development, and with different historical and cultural backgrounds may see this issue of human rights from different perspectives," he said.
During the trip, which finishes on Wednesday, investors will be looking for any signals that Li, number two in the ruling Communist party, may send about the future of Asia's largest economy in two speeches he is due to give before leaving. ($1 = 0.5956 British Pounds)
(Writing by Guy Faulconbridge and Andrew Osborn; Additional reporting by Ben Blanchard and Aizhu Chen in Beijing,; Saikat Chatterjee in Hong Kong, Vladimir Soldatkin in Moscow,; Oleg Vukmanovic in Milan and Nina Chestney in London; Editing by Mark Trevelyan)