LONDON (Reuters) - British engineer Cobham said it would cost an additional $53 million (£40 million) to complete its work on Boeing's troubled KC-46 aerial refuelling programme, with delays straining ties between the two groups and sending its shares down 10 percent.

Cobham, Britain's third biggest defence and aerospace group after Rolls-Royce and BAE Systems, said completion of the programme could take significantly longer than planned, a delay which has angered Boeing, the world's largest planemaker.

As a result, Cobham said Boeing had made "as yet unquantified damages assertions" relating to the programme, prompting the U.S. group to withhold payment for Cobham's work. The British group is disputing the assertions.

Cobham said it would take an additional non-underlying charge of about 40 million pounds in its interim results for 2018 in order to finish the project. It said it would release those results on August 3 and did not expect to announce any change to its underlying profit guidance.

Its shares were down 10 percent at 118.5 pence.

Boeing's shares were hit on Wednesday when it reported $426 million in higher costs related to the long-delayed programme.

Cobham, which made its name in the 1930s developing air-to-air refuelling techniques, was hit by a string of profit warnings in 2016 and 2017, forcing it to raise cash from investors.

It has since sold assets to cut debt and stabilised the business under new management.

Analysts at Jefferies said they thought it was unusual and tough for Boeing not to pay for deliveries. It said Cobham's further exposure may be limited however by the fact the parts are delivered to the U.S. Air Force, not Boeing.

(Reporting by Kate Holton, Editing by Paul Sandle and Angus MacSwan)