US drugmaker AbbVie raised its offer for Shire to £51.15 a share on Tuesday, hoping to win over its reluctant target after an earlier offer was rejected.

The London-listed hyperactivity and rare diseases specialist said AbbVie’s previous £46.26 cash-and-stock proposal, worth some $46 billion, had fundamentally undervalued the company.

AbbVie is eager to buy Shire both to reduce its tax bill by moving its tax base to Britain - a tactic known as inversion - and to diversify its drug portfolio. The company currently gets nearly 60 per cent of its revenue from rheumatoid arthritis drug Humira, the world's top-selling medicine, which loses US patent protection in late 2016.

Chief executive Richard Gonzalez has pressed the case for his pursuit of Shire in a series of meetings with shareholders on both sides of the Atlantic, after setting out the strategic rationale for a deal on June 25th.

Reuters