Bradshaw is the son of a former Anglican vicar of Norwich Cathedral Canon Peter Bradshaw and his wife Daphne Murphy. Bradshaw was educated at Thorpe Grammar School, followed by the University of Sussex where he read for a degree in German. He also attended the University of Freiburg in Germany while an undergraduate. Between 1982 and 1983, Bradshaw taught English at the Technikum, a school of Technology in Winterthur in the Zurich canton of Switzerland.
Bradshaw became a reporter with the Exeter Express and Echo in 1984 and subsequently joined the Eastern Daily Press in Norwich as a reporter in 1985. In 1986 he joined the staff of BBC Radio Devon and became the Berlin correspondent for BBC Radio in 1989 and was working in the city when the Berlin Wall fell. In 1991, he became a reporter with BBC Radio's The World At One, contributing to the programme until his election to Westminster. He won the Sony News Reporter Award in 1993.
The sitting Conservative MP, John Hannam had retired and the Conservatives chose Adrian Rogers to be their candidate. While Bradshaw is openly gay, Rogers is a leading member of the religious right. The campaign was vitriolic and bitter with allegations of homophobia and sin. The result, however, was not close, and Bradshaw was elected as the Labour MP for Exeter with a majority of 11,705. He made his maiden speech in the House of Commons on 4 July 1997. He was the second British MP who was openly gay at the time of first election, 21 minutes after Stephen Twigg.
In the Commons, Bradshaw introduced the Pesticides Act in 1998, which gave more powers to inspectors. He became a Parliamentary Private Secretary to the Minister of State at the Department of Health John Denham in 2000.
After the 2001 general election Bradshaw entered Tony Blair's government as the Parliamentary Under Secretary of State at the Foreign and Commonwealth Office. Only days after being appointed to the Foreign Office, he had to answer questions following the terrorist attacks of 11 September 2001. On 6 March 2002, while answering Parliamentary Questions, Bradshaw accused George Galloway of "being not just an apologist but a mouthpiece for the Iraqi regime over many years". Galloway responded by accusing Bradshaw of being a liar, though after a suspension of the Commons sitting, both men withdrew their comments.
Bradshaw became the Deputy to the Leader of the House of Commons Robin Cook in 2002, and was an Under Secretary of State at the Department of Environment, Food and Rural Affairs from 2003 until 2006, when he was made a Minister of State at the same department. During this period, he was sent to Brussels to negotiate changes to the Common Fisheries Policy on behalf of the British in-shore fishing fleet. When questioned, on Newsnight Scotland, by Gordon Brewer, as to the progress of these negotiations, he was unwilling/unable to answer questions relating to his brief, such as the size of the Scottish inshore fishing fleet, or the catch quotas relating to particular species.
His plan to introduce private management of some NHS trusts was also heavily criticised. The BMA called it a step towards privatising the NHS, Dr. Jonathan Fielden observed that there was no evidence private management was better than public sector management, commenting "How many of us have seen our Trusts bring in the management consultants, paying through the nose, only to get a half baked solution and one that the real talent in the NHS could have delivered for less?", Professor Allyson Pollock, head of the Centre for International Public Health Policy at the University of Edinburgh, said: "Bringing private management in will simply accelerate the process of privatisation of services which will have catastrophic effects for the patients and the public at large. It will mean less care for everyone, and more money for profits and shareholders". Nigel Edwards, of the NHS Confederation, said the government had tried drafting in private sector management before - at the Good Hope Hospital in Sutton Coldfield in 2003 - which was not successful. He commented: "What it revealed is that the reason that hospitals tend to fail is often much more complicated and much more difficult than just poor management".
On 24 June 2006, Bradshaw and his partner Neal Dalgleish, who is a BBC Producer, registered a civil partnership. He was one of the first MPs to do so, and he was the first Cabinet Minister to be in a civil partnership. Bradshaw wants the position of the Church of England over same sex marriage or partnership in the clergy clarified. Specifically he wants to know if a member of the Church of England clergy who married a same sex partner would be disciplined or defrocked.
On 28 June 2007, he was moved to become a Minister of State in the Department of Health and, in addition, was given the Minister for the South West portfolio.
In 2009, Ben Bradshaw won the Stonewall Politician of the Year Award in 2009 for his work to support equality for lesbian, gay and bisexual people. He was given a score of 100% in favour of lesbian, gay and bisexual equality by Stonewall. Bradshaw was sworn in as a member of the Privy Council of the United Kingdom in 2009, giving him the right to the honorific prefix "The Right Honourable".
On 7 October 2010 the Labour Party announced that he had failed to be elected to one of the 19 available places in the first Shadow Cabinet of new leader Ed Miliband. On 5 February 2013, he voted in favour in the House of Commons Second Reading vote on the Marriage (Same Sex Couples) Bill.
Following Labour's defeat in the 2015 general election, and the resignation of both Miliband and deputy leader Harriet Harman, Bradshaw announced his intention on 15 May to stand in the Labour Party deputy leadership election. He later gained the minimum 35 nominations required to stand in the ballot with the other candidates. Bradshaw came last in the election.
Bradshaw claimed during a Commons debate in December 2016 that it is "highly probable" that the result of the Brexit referendum was manipulated by Vladimir Putin.