"If you can agree on this, as well as on robust commitment towards a level playing field, and the necessary enforcement regime... we will achieve a very ambitious free and fair trade agreement", said Barnier.
The figures underline the large number applications for the scheme, which was launched nationally in March a year ago, but also the challenge ahead for the government to ensure all European Union citizens correctly apply.
Mr Barnier told reporters in Brussels: "It's clear that the agreement that we wish to have in the interests of United Kingdom fishermen and in the interests of European fishermen - I call that reciprocal access to our territorial waters and our markets - that agreement on fisheries will be inextricably linked to the trade agreement, as indeed will be... the agreement on the level playing field agreed with Boris Johnson". "With an implementation period until December 2020, this would give businesses stability, certainty and time to prepare for our new relationship after EU Exit".
As Britain seeks to leaves the European Union, it will again need to find a new relationship with it at a time when the future of the USA commitment to Europe is also uncertain.
He is also expected to say that if the European Union does not accept an agreement similar to the EU's arrangement with Canada, then trade with the EU will have to be based on the UK's existing withdrawal agreement with the bloc, which would be "more like Australia's".
He said that "where there's a will, there's a way" to reach a deal.
Regaining control of Britain's rich fishing waters was a totemic issue for many Brexit campaigners. This is an extension of its overall stance that the negotiations can not be broken into smaller parts on which it might be easier for Britain to win concessions.
The British government has rejected this because, it says, the European Union court would not be a neutral arbiter.
Currently, Australia-EU trade runs along basic World Trade Organization rules, although there are specific agreements for certain goods.
British Prime Minister Boris Johnson said that it was now the EU's turn to fall in line with the UK's expectations.
"If the request is to have broad access to a market of 450 million European consumers, zero tariffs, zero quotas".
Johnson's speech was shorter on detail than his EU counterparts, but he played down the need for any assurances on the EU's demands, stating that "we are not leaving the EU to undermine EU standards, there will not be a ruthless race to the bottom, we will not engage in any kind of dumping", he said.
However, the EU's position is that it will not be included in the negotiations, and any separate agreements on Gibraltar - over which Spain has territorial claims - would require approval from Madrid.