The tug of war for the control of Lloyd's insurer Limit intensified this week after Australian insurer QBE topped a rival cash bid from Wellington Underwriting.

QBE decided to raise the stakes on Friday, when it increased its cash offer from 120p to 135p per Limit share, which is believed to value the company at around £360m.

The counter-bid is above Wellington Underwriting's recent cash offer of 133.5p per share plus convertible loan stock.

However, Limit chairman, Jonathan Agnew, insisted it was his understanding that QBE's bid had now lapsed. This he said was because it rested on the precondition that Limit's board would recommend the company enter into certain financial arrangements which it had declined to do.

Limit's board of directors also said in a statement that it believed a merger with Lloyd's insurer Wellington would provide better value for money to shareholders through efficiency savings.

A merger of Wellington and Limit would create the largest independent underwriting company at Lloyd's, with a capacity of £1.2bn.

The statement from Limit said: "The board of Limit believes that the Wellington proposal is in the best commercial interests of Limit. The board therefore continues to support the Wellington proposal and is working with it to put this to Limit shareholders as soon as possible."

Limit has rejected two previous offers from QBE.

QBE said it was currently waiting for a formal response from the board of Limit.

A statement from QBE indicates the bidding war for Limit is set to continue. It said: "QBE reserves the right in the event this proposal is rejected to take further action as it deems appropriate."

The Australian insurer achieved recent success on the acquisition trail with the purchase of Iron Trades for £175m last December.