Adds details on KKR offer in paragraph 8, shares in paragraph 7, background throughout

July 2 (Reuters) - British scientific instruments maker Spectris SXS.L has agreed to a takeover offer from U.S. investment firm KKR KKR.N valuing it at 4.7 billion pounds ($6.46 billion) including debt, and has withdrawn its support for a rival offer from Advent.

The battle for Spectris, Britain's largest takeover target this year, heated up after KKR last week tabled a bid valuing Spectris at 40 pounds per share including dividends, 6.3% higher than Advent's 37.63 pound per share offer, which valued the group at 4.4 billion pounds.

Spectris said its board has decided to withdraw its recommendation of Advent's offer in favour of the higher bid from KKR, which had made two prior takeover proposals for the London-listed firm. The firm had rejected KKR's second takeover bid on June 13.

Advent, which had reserved the right to increase its offer for Spectris if a competing bid was made, did not immediately respond to Reuters' request for a comment.

"The ball is now back in Advent's court, and having stalked Spectris for an extended period, there must be some chance that it keeps fighting," analysts at Stifel said.

"But having already raised its bid several times, room for manoeuvre looks fairly limited to us."

Spectris shares climbed as much as 5.3% to 40.32 pounds on Wednesday to their highest in more than three and a half years. As of Tuesday's close the stock had surged nearly 88% since Advent's initial bid was disclosed on June 9.

In its latest offer for Spectris, shareholders will receive 39.72 pounds per share in cash from KKR and an interim dividend of 28 pence.

Britain's cheap valuations and relative stability have lured overseas buyers. KKR was also involved in a bidding war for British healthcare real estate investor Assura AGRP.L, which agreed a deal with KKR-Stonepeak before ditching them in favour of a higher bid from Primary Health Properties PHP.L last month.

($1 = 0.7281 pounds)

(Reporting by Raechel Thankam Job in Bengaluru; Editing by Eileen Soreng, Sherry Jacob-Phillips and Jan Harvey)

((Yamini.Kalia@thomsonreuters.com;))