In 1976, Dorfman started his own currency exchange Business from one small shop based in Southampton Row in central London. The company spread to ports overseas, initially in the Netherlands and Belgium. In 1986, Dorfman won Travelex a landmark contract as the first non-bank foreign exchange provider at the newly opened Heathrow Terminal 4. The company expanded into airports worldwide, opening in the USA in 1989 shortly followed by Australia in 1990.

In 2001 Dorfman was the winner of the Consumer Business Category in the UK "Entrepreneur of the Year" awards sponsored by Ernst & Young, Citibank and The Times. In 2002 he received the British American Chamber of Commerce's UK Entrepreneurial Award, and the Institute of Economic Affairs' Free Enterprise Award. In 2007 he received the Honorary Australian of the Year in the UK award.

Travelex pioneered sponsorship deals including Travelex Cheap Ticket Season at the National Theatre, as well as sponsoring the winning World Cup teams for Australian Cricket in 2003 and England Rugby the same year.

In addition, he is a trustee of the Royal Opera House, of the Royal Academy Trust and of JW3; deputy chairman of the Community Security Trust, and was a governor of St Paul's School from 2005 to 2016.

He was also on the board of the Royal National Theatre from 2007 to 2015, and the National Theatre's Cottesloe was renamed the Dorfman Theatre in 2013 following a gift of £10 million towards the National Theatre Future redevelopment project.

In 2008 Dorfman was appointed CBE in the Queen's Birthday Honours list for services to Business and charity. In 2011, he was awarded The Prince of Wales Medal for Arts Philanthropy. He is an honorary fellow of St Peter's College, Oxford and an Honorary Bencher of Lincoln's Inn. He was awarded an honorary doctorate by Buckingham University in 2016.

Dorfman is a minority shareholder in The Office Group, the British pioneers of co-working spaces. He was previously chairman and majority shareholder of the company from 2010 to 2017, before a £500 mn deal with Blackstone in June 2017. The Group has over 30 buildings across central London. Its clients include thousands of small businesses and start-ups as well as larger companies. In 2014, he co-founded and became chairman of Doddle, a Retail Business enabling people to collect, return and send their online shopping from train stations and elsewhere. Dorfman is also a lead investor and board member of the London Theatre Company.

Travelex sold its card programme management Business to MasterCard for £290 million in 2011, and then its Global Business Payments to Western Union for £606 million. In 2014, an agreement was reached to sell Travelex to shareholders in Abu Dhabi, Dorfman however, still retains a 5% shareholding.

In 2017, following a gift from the Dorfman Foundation, the Royal Academy announced the launch of two new international architecture awards, and the restoration of the Senate Rooms in Burlington Gardens to house a new architecture space and café.

Dorfman is chairman of youth and enterprise charity the Prince’s Trust, having joined the charity's Council in 2007. He is also the chairman of Prince’s Trust International, which aims to help unemployed young people around the globe into education, training and work.