Britain's largest building society, Nationwide, has proposed a £2.9 billion ($5.7 billion) cash offer for Virgin Money, removing it from the ASX.

The offer of £2.20 ($4.25) per share, including a 2 pence dividend, represents a 38% premium to Virgin Money's closing price on March 6.

The merger would make Nationwide the second-largest provider of mortgages and savings in the UK, with assets totalling £366 billion ($707 billion) and lending of £284 billion ($548.62 billion).

 The phased-out Virgin Money brand will see integration over the next six years.