TSB is offering a £30 discount to customers who take out its Pick and Protect combined buildings and contents insurance.
Customers can also get a further £5 discount by bolting on extras such as cover for their bicycle or gadgets.
The offer is available to anyone who gets a quote from TSB until 31 October.
Pick and Protect home insurance allows customers to only pay for the cover they want – and to add or remove cover at any time without being charged admin fees.
Customers are not charged extra for paying monthly and anyone making a claim gets their own dedicated claims manager from the moment they call up.
TSB is also offering to pay customers’ cancellation fees up to £100 if they switch their home insurance to TSB.
Research carried out by TSB shows that seven of the top 10 home insurance providers in the UK charge a cancellation fee, costing around £22 on average.
Kat Robinson, TSB’s head of general insurance, said: “We know that one size doesn’t fit all. That’s why our Pick and Protect home insurance provides customers with the home insurance they want, when they want it.
“As Britain’s challenger bank we’re trying to do something different to help make the home insurance market work in the interest of consumers.
“We don’t charge cancellation fees on our home insurance products, and TSB’s cancellation fee refund service also ensures that customers aren’t left out of pocket when they switch to us.
“And now, our £30 multi-cover discount for building and contents insurance offer, gives people another reason to get a great deal on their home insurance by switching to us.”