Meanwhile, the EU's chief negotiator Michel Barnier warned that the UK's withdrawal agreement could still fail over the issue of the Irish border, leading to an "extremely serious" no-deal Brexit.
Speaking on BBC Radio 4's World at One, Mr Collins said: "We were told after the 2016 referendum, during the 2017 general election and afterwards by the Government that we would take control of our waters just like any other natural resource in March 2019".
Mr Tusk added: 'I feel we are closer to the final solutions and the deal.' But Mrs May looked an isolated figure after a photo emerged of European Union leaders, including Germany's Angela Merkel and France's Emmanuel Macron, having a drink without her on Wednesday.
British Prime Minister Theresa May had earlier addressed her fellow leaders, indicating that she could accept extending the post-Brexit transition phase to take the heat out the deadlocked issue of the Irish border.
But after urgent talks on the Irish border ended Sunday without producing a breakthrough, Wednesday's gathering looked more like a therapeutic bonding session than an occasion to celebrate.
France did not rule out a possible lengthening of Britain's post-Brexit transition period if it helps advance negotiations with London, but any extension would come with conditions, an official in President Emmanuel Macron's office said on Thursday.
Mr Barnier said there was absolutely no intention by European leaders to punish Britain.
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The transition - during which the United Kingdom would remain in the single market and customs union and subject to EU rules - is meant to provide time for authorities and officials to prepare for new arrangements following the official date of Brexit in March 2019.
Tom Newton Dunn, political editor of the Sun newspaper, commented that May saying a transition extension would only be for a few months feels like the "I'm only half pregnant" defense.
"I think we are quite close to a no-deal", warned Konrad Szymanski, the Polish minister for European Affairs, after a pre-summit meeting with his European counterparts in Luxembourg.
"The last stage will need courage, trust and leadership on both sides", May told her European Union counterparts.
"The negotiations are very much about a solution and we have got to the point where they have become very technical but certainly it's something that is in the back of my mind as a potential outcome if we get this wrong", he said.
In her news conference Mrs May appeared to rehearse the arguments she will likely use to argue back against those criticisms - that the idea isn't new, that it wasn't requested by the United Kingdom, but that it is worth considering if it opens up the blockage of the Irish backstop.
It emerged on Wednesday that Mr Barnier was ready to discuss a further year's extension to allow time to find a solution to keep the Irish border open.
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Leaders of other member countries said the real fight was not with the European Union. but within May's fractured Conservative Party.
Accepting that would mean extending the period during which Britain would be "bound by European Union laws" while having no representation until December 2021. Now we know our limits: we don't want an agreement which calls into question the integrity of the single market, or the four freedoms, or which does damage to Ireland.
All governments insist, though, that they want a deal in the coming weeks that can avoid chaos when Britain leaves in March.
Tory MP Nadine Dorries repeated her call for former Brexit secretary David Davis to replace Mrs May as leader. "They do not know themselves what they really want".
But with talks at an impasse, the bloc has suggested extending that period to provide more time to strike an agreement that ensures the border between Northern Ireland and the Republic of Ireland remains friction-free.
The chaos promised by "no deal" is very much in the minds of officials on both sides of the Channel.
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