The affected shows are those in High Wycombe, Tunbridge Wells, Derby, Northampton, Oxford and Southend.
The band posted the following on their website:
"We are very saddened to announce that Dave has been suddenly admitted to hospital due to complications with his lung. He has to have an operation on Thursday (26 Feb) to fix the problem. This means we have had to postpone the first part of the tour. Dates are to be re-arranged and tickets already purchased will be valid. We are so sorry and utterly gutted. Dave just cannot believe this has happened. At the moment the rest of the tour still stands. Dave is due out of hospital on Sunday, we will keep you posted on his recovery and the remaining dates."
Line hopes to recover in time for the band's show at London's 100 Club on March 9th, which is sold out by the way.