UK Prime Minister Theresa May | Photo credit: Press Association
Sajjad Karim's comments come after UK Prime Minister Theresa May on Wednesday ruled out a possible second referendum on British membership of the EU.
In a "get tough" approach to the Remain camp, May told a cabinet meeting, "We must continue to be very clear that 'Brexit means Brexit', that we're going to make a success of it.
"That means there's no second referendum; no attempts to sort of stay in the EU by the back door; that we're actually going to deliver on this."
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She also ruled out holding a vote on leaving the EU in the UK Parliament, where many MPs oppose the move.
The British government also again said on Wednesday it would not accept free movement of EU workers after Brexit, but still wanted "unique" access to the single market.
Reacting to May's remarks, Karim, said, "May is rightly giving full commitment of the Prime Ministers' office to allow Boris Johnson, Liam Fox and David Davies an absolute unqualified opportunity to deliver on the promises they made to the British people in the referendum. They therefore have no excuse not to deliver on those promises."
He added, "Difficulties will emerge if their delivery diverges from their promises and whether this will be acceptable as a form of Brexit.
"Exiting Britain into a vacuum will not be acceptable to the Prime Minister so it is now really time for leading Brexiteers to come up with the goods and present the alternatives to EU membership."
Further comment came from UK Tory MEP Dan Dalton, who, referring to May's address to the cabinet, said, "I think this is just restating the UK government position since the referendum.
"But I think any more uncertainty, like speculation of a second referendum or that Brexit won't happen just makes it much harder to get a position together and to even start the negotiations. I don't think that uncertainty is in anyone's interests at his stage."
Elsewhere, Ashley Fox, the leader of the Conservative delegation in the European Parliament, told this website, "The EU referendum result sent a clear message to Westminster and the Prime Minister was absolutely right today to, once again, spell out her determination to implement the will of the British people.
"May understands that total commitment is going to be required to make Brexit work and ensure that Britain thrives outside the EU."
Another British MEP, Glenis Willmott, leader of the Labour delegation in the European Parliament, said, "The UK government needs to be honest about what leaving the EU entails, and it needs to set out the consequences of the different courses of action.
"During the referendum, Leave campaigners claimed we could remain in the single market and not have to abide by the rules - that we could have our cake and eat it.
"Yet we now seem to be facing the prospect of leaving the single market which would lead to tariffs and other negative consequences for the British economy.
"May must be honest about her objectives in the negotiations to come, and more inclusive in her efforts to achieve it. The outcome of Wednesday's discussion in cabinet must also be brought to the UK Parliament for scrutiny.
"Leaving the EU will be the biggest change in our lifetime, and will affect our country for generations to come. It cannot be left to Tory hardliners to determine how this is done, and must not be pushed through without proper democratic scrutiny."
The MEPs' comments come after European Commission First Vice-President Frans Timmermans this week expressed frustration that the UK, two months after the referendum, still had no detailed Brexit plan.
The Dutch official said, "They should get their act together and tell us what they really want out of this. The onus is on the country that decides to leave to tell us how they want to leave."