WASHINGTON (Reuters) - U.S. Trade Representative Michael Froman said on Wednesday that China's latest offer in bilateral investment talks is "a fair distance away from being acceptable," but warrants continued engagement with Beijing.

Froman, in a Bloomberg Television interview, also said that it may be possible for Britain, once it separates from the European Union, to join the 12-country U.S.- and Japan-led Trans-Pacific Partnership (TPP) trade deal.

Froman said that Beijing's latest "negative list" of sectors that it wants to keep off-limits from U.S. investment presented last month is a "serious effort" that shows Beijing is trying to work through difficult issues to open up its economy.

"It is still a fair distance away from being acceptable to us, but we are going to continue engage the Chinese and underscore for them the kinds steps that are going to be needed both for the negative list and in terms of what kinds of disciplines we need to put in the text to create a high-standard agreement," Froman said at an investment banking conference in Sun Valley, Idaho.

Regarding Britain's referendum to leave the EU, Froman said that would not slow down talks with the EU towards a major U.S.-European trade deal, the Trans-Atlantic Trade and Investment Partnership (TTIP).

He said that it would be difficult for the United States to consider negotiating a separate trade deal with Britain "until you know what its relationship with the EU is going to be," adding that much depends on whether London pursues a model based on full sovereignty over regulation and tariffs.

"We're certainly going to want to do whatever we can to deepen our relationship with the UK and as well as with the EU, and ultimately that could mean the UK joining TTIP when it's completed," Froman said. "And I've even heard some people suggesting that they could join the TPP."

He said the idea of the UK joining the completed trade deal that is awaiting approval by the U.S. Congress is one of "multiple ideas" circulating for a new U.S. trade relationship with the UK. The 12 TPP countries represent about 40 percent of global economic output.

(Reporting By David Lawder; Editing by Sandra Maler)