The group, which has a £10 billion loan book, has launched Paragon Bank with an initial investment of £12.7 million, with more funds to come over time to support growth.
As a new retail-funded lending bank, it is offering car finance through brokers and dealerships from today, followed by savings products through a direct online platform from the spring.
Personal loans, offered through intermediaries, will launch later in the year while other finance options for consumers and small businesses are expected to be developed in the future.
Paragon chief executive Nigel Terrington said: "Paragon Bank will bring choice and customer focus to the UK banking market, by providing consumers with straightforward, competitive products that are transparent, easy to understand and manage.
"Initially, Paragon Bank will focus on lending in sectors where Paragon has extensive experience and previous success, in markets which are displaying good growth opportunities."
"Paragon Bank's aim is to establish itself as a trusted banking partner for its customers and business partners."
Paragon made the announcement following approval from the Bank of England's Prudential Regulation Authority. The bank is led by Richard Doe, previously chief executive of ING Direct UK.
Its existing businesses include a property loan arm focused on buy-to-let mortgages for landlords and residential property investors, and an investment division, Idem Capital, purchasing UK consumer debt.
The move comes amid calls for more competition and choice in the banking sector and new challenges from a number of smaller players to the big names in the industry.
Earlier this month, supermarket Sainsbury's took full control of its banking arm after acquiring a 50% share from Lloyds Banking Group. Meanwhile, Tesco Bank set out plans in December to expand into the current account market.
Elsewhere, Metro Bank, which has 25 branches in the UK, plans to open up to 12 new sites during this year.
Last year, Lloyds Banking Group hived off more than 600 branches using the revived TSB brand ahead of a planned stock market float.
And Royal Bank of Scotland has announced plans to spin off more than 300 sites under the Williams & Glyn name.