The announcement kicks off a three-day visit by Li during which Britain aims to strengthen trade ties and warm a relationship strained by a spat over Tibet.
The changes include a single visa to allow Chinese and Indian tourists to travel to both Ireland and Britain, and a simplified online application form for independent travellers.
Britain is also in talks with European partners to allow Chinese visitors to apply for visas for Britain and Europe's 26-country Schengen Area through a single application process, following a 2013 pilot programme with tour operators which sped up applications.
The moves are likely to please retailers keen to attract Chinese shoppers, who are the world's biggest spenders on luxury goods by nationality but do two-thirds of their luxury spending abroad, where high-end items are cheaper, according to Bain & Company consultants.
Britain opted out of membership of the Schengen Area in order to maintain control of its borders, and Prime Minister David Cameron has pushed for tighter restrictions on movement within the European Union as part of a bid to cap immigration, a touchstone issue for his coalition government.
"But I want to make sure they are as efficient as possible in welcoming tourists and business people from around the world."
The introduction of a priority visa service and the opening of 12 visa application centres across China had contributed to a increase of nearly 40 per cent in the number of visas issued to Chinese visitors between 2012 and 2013, the Home Office said.
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