The Conservative Party and Labour Party, who both support leaving the single market and scrapping free movement of people, hold 580 of the 650 seats.
Jack Straw, a former Labour foreign minister, said the result means there will now be a lot of pressure in parliament for a soft Brexit.
Theresa May has apologised for the election result.
But opposition politicians and some members of her own party have called on her to quit. She will remain the Prime Minister for now, assuming that she can form a government with the DUP party of Northern Ireland.
"I'm never going to give in arguing for what I believe is a pathway to a majority Labour government", he added. Even the idea that a vote for the Labour Party could be seen as some sort of "protest" is not necessarily borne out by the evidence.
On Twitter, Siegfried Muresan, spokesman for the European Parliament's largest grouping, the European People's Party, said, "EU did not want #Brexit, but has been prepared to negotiate it since a year ago".
He had annoyed many Conservatives who want a clean break with the European Union by stressing the need for a Brexit deal that allows companies to keep on hiring the migrant workers they need, and took the blame for a policy U-turn in March when he quickly dropped a plan to raise social security tax for self-employed workers. Instead, she has left Britain's government ranks in disarray, days before the divorce negotiations are due to start on June 19.
Mrs May had spent the campaign denouncing Mr Corbyn as the weak leader of a spendthrift party that would crash Britain's economy and flounder in Brexit talks, while she would provide "strong and stable leadership" to clinch a good deal for Britain. Their MPs, as radical Irish nationalists, do not take their seats in the British parliament, so the more of them there are, the fewer seats a party parliament effectively needs to win a majority. On Friday, May was expected to appoint a team that will take on one of the most demanding negotiations in British history.
The election results create uncertainty surrounding the negotiations over Britain's exit from the European Union.
"Theresa May is certainly the strongest leader that we have at the moment", David Jones, a junior Brexit minister, told the BBC.
Former Conservative minister Anna Soubry added that the premier "is in a very hard place. she now has to obviously consider her position". Following the failed 2014 independence referendum, the Nationalists won 54 out of 57 Scottish seats in 2015; a key component of their campaign this time was to get a new independence referendum as early as next March.