Insurers paid out more than £8m every day in 2013 in individual life, critical illness and income protection claims, a daily £2m increase compared with 2012, the ABI revealed.
Mr Grant said this figure should both reassure consumers and demonstrate the importance of comprehensive cover.
He added: “People should continue to be encouraged to think about their protection needs and whether they can afford to leave their families unprotected. A loss of income through being unable to work, falling ill or a death in the family takes not only an emotional toll but a financial one too.”
Around 97 per cent of all claims were paid in 2013, according to the ABI.