Moneysupermarket said the 'Brexit' vote may trigger rising energy prices, higher insurance costs and lower interest rates - good for homebuyers but not for savers.
Chief executive Peter Plumb urged consumers to use price comparison services to offset the potential impact "in the turbulent years ahead".
"As UK families prepare for life after the 'Brexit' vote, with potentially rising energy prices, rising insurance prices and lower interest rates, our trusted brands and services will be there to make sure household bills are as low and easy to switch as possible," he said.
Plumb said Moneysupermarket made another strong start to the year, increasing revenues by 10% and saving customers a record £890mln.
The group expects half-year revenues to rise 10% to £158mln and adjusted operating profit to increase by 6% to about £54mln.
In the second quarter, demand for insurance products picked up and balance transfer credit cards drove sales in its money arm.
MoneySavingExpert and TravelSuperMarket performed in line with expectations.
Plumb said: "Moneysupermarket is a pure play digital business, with a strong balance sheet and a new technology platform."
Shares in the group rose 20.2p, or 7.5%, to 290.9p in mid-morning London trading.
Broker Shore Capital, which is advising investors to buy the shares at 234p, said in a note: "We are encouraged by the strong trading momentum flagged in this morning’s update and particularly the improved performance reported in insurance.
"We are bullish on MONY’s long-term fundamentals."