LONDON, Jan. 29 (Xinhua) -- British business continued showing their frustration over still unclear Brexit prospect, though Prime Minister Theresa May was closer than ever on Tuesday to finally reaching an elusive Brexit deal.

Carolyn Fairbairn, director general of the Confederation of British Industry (CBI), which represents businesses employing one-third of the private sector workforce, said: "Another deeply frustrating day for business. Renegotiation is a throw-of-the-dice, it must succeed or fail fast."

"Rejecting no deal is welcome but doesn't get a deal. Until MPs can agree a solution, the threat of no deal will continue to drain money from the UK," she wrote on twitter.

The British House of Commons voted for an amendment that tells the government to ask the European Union to delay Brexit if no deal had been passed in Parliament by the end of February, not specifying how long.

Adam Marshall, director general of the British Chambers of Commerce, said: "Another day lost while the clock is ticking. Government and parliament are still going round in circles when businesses and the public urgently need answers," according to newspaper The Guardian.

Stephen Martin, director general of the Institute of Directors, said on twitter that MPs have managed to form a majority in each vote, but the path ahead is still far from clear.

By 317 votes to 301, MPs in the House of Commons gave their backing to May's deal which they rejected earlier this month, providing changes are made to the so-called Irish backstop border issue.

The 16 majority for her deal gives May a mandate to return to Brussels to call for a re-opening of negotiations, and indicates that the Brexit deal is likely to win the critical final vote in British parliament if changes are made to the Irish border issue.

Mike Cherry, national chairman of the Federation of Small Businesses, said that neither small businesses nor the country are ready for the scenario.

"We cannot lose sight of the reality that we are still no closer to securing a pro-business deal before 29th March," he said, quoted by The Guardian.