Adds graphics and detail in paragraphs 3,4,6,8

July 20 (Reuters) - U.S. warehouse company Prologis PLD.N said on Monday that Segro SGRO.L rejected its latest £13.5 billion ($18.17 billion) takeover bid, urging its British rival's shareholders to push for its board's engagement ahead of a formal deadline.

Segro's board unanimously rejected the proposal — Prologis' third — on July 17. The bid values Segro at £9.93 per share and consists of 0.0890 new Prologis shares for each Segro share plus a partial cash alternative of up to £2.7 billion, Prologis said.

The latest proposal is at close to a 34% premium to the group's closing price on June 23, a day before Prologis first went public with its interest.

Prologis added that, under the proposed combination, it intends to explore the feasibility of a secondary listing of its shares on the London Stock Exchange.

Segro spurned the U.S. firm's initial £12.6 billion all-share proposal in June, saying it was "opportunistically timed" and significantly short of fair value. A second proposal was rejected on July 12.

The latest rejection has prompted Prologis, known for acquiring warehouse-focused REITs, to take its case directly to Segro's shareholders as British takeover rules dictate it has until July 22 to make a firm offer or walk away.

Segro did not immediately respond to a Reuters request for comment on Prologis' statement, which was issued outside UK business hours on Monday.

UK-listed companies have become the focus of growing international interest as British firms trade at relatively low valuations, with easyJet EZJ.L and Intertek ITRK.L among the blue-chip companies attracting takeover interest in recent months.

($1 = 0.7431 pounds)