"If it goes very slow, as is the case for the moment, it will be very hard to say that there is sufficient progress when we are in October", he told MEPs.
He said there was a need to be "crystal clear" that negotiations on the new post-Brexit relationship, particularly the economic and trade relationship, would not be carried out before issues relating to financial obligations, citizens' rights and Ireland are dealt with.
Junker said the United Kingdom "hesitates showing all its cards" but said "none" of the government's position papers was "satisfactory".
Barnier and British negotiator David Davis appeared at a short media briefing before they started negotiations.
Britain feels it is in a good position in Brexit negotiations and wants to agree with the European Union to move on to discussions about its future relationship by October, Prime Minister Theresa May's spokeswoman said on Tuesday.
In Westminster's broader view, a future trade deal and mutually-beneficial economic ties would suffice to make up for the Brexit payment the European Union requires.
He added: 'I did read, with the requisite attention, all the papers produced by Her Majesty's Government and none of those is actually satisfactory. During his speech, the EC's president also said that the decision to finally end Ankara's European Union entry attempts depends entirely on Turkish President Recep Erdogan. "First of all we settle the past before we look forward to the future".
Meanwhile, Labor's new Brexit stance was branded chaotic by one of the party's Leave-supporting MPs.
Echoing David Davis' calls for Brussels to show greater flexibility in its approach to Brexit discussions, the Prime Minister has repeated assertions that Britain is "in a good position" and ready to "move on" to negotiating its future trade and security arrangements with Europe.
Officials on both sides have said the talks would center on technical issues and would not create any major breakthroughs.
Starmer said: "There's a growing consensus on both sides of the Channel that it's extremely unlikely that a bespoke transitional period can be negotiated, agreed and implemented by March 2019".
Spain's decision to boost staff at a national level comes after the European agency initiated a business continuity plan earlier this month to deal with the uncertainty and workload implications linked to Britain's withdrawal from the EU.