The EU has published no-deal Brexit contingency plans as trade talks hang by a thread.
Boris Johnson and European Commission President Ursula von der Leyen set a deadline of Sunday for deciding whether to proceed with deadlocked negotiations.
President von der Leyen told EU leaders on Thursday to prepare for a no-deal Brexit on January 1 as she published a list of new contingency plans to mitigate the disruption.
But No10 immediately rejected the suggestion of a 12-month reciprocal fishing arrangement.
Fishing has proved to be one of the big stumbling blocks to progress, as it is regarded as a totemic issue by Brexiteers.
EU countries such as France are keen to maintain access to UK fishing waters but negotiators have clashed over fishing quotas.
The Prime Minister's spokesman said: "As we've said throughout the negotiations, once we leave the end of the transition period, we will take back control of our waters.
"We would never accept arrangements and access to UK fishing waters which are incompatible with our status as an independent coastal state."
He said the UK would "look closely" at the mini-deals proposed by the EU if there is no-deal.
Other measures proposed would ensure basic reciprocal air and road access between the EU and the UK for six months.
Aviation safety certificates would continue to apply to prevent the grounding of aircraft.
Another measure would cover freight and passenger travel on the roads for six months, as long as the UK reciprocated.
In a statement, President von der Leyen said: “Negotiations are still ongoing.
"However, given that the end of the transition is very near, there is no guarantee that if and when an agreement is found, it can enter into force on time.
"Our responsibility is to be prepared for all eventualities, including not having a deal in place with the UK on 1 January 2021."
It comes after the Prime Minister made an eleventh-hour dash to Brussels on Wednesday to try to jump-start the stalled talks.
After a three-hour dinner, both sides said they would decide on Sunday whether talks for a EU-UK trade deal could continue.
Downing Street sources said it was unclear whether a deal could be agreed, as significant differences remain between both sides.
If a trade agreement cannot be hammered out, the UK will be forced to revert to damaging World Trade Organisation terms from January 1, when the Brexit transition period ends.
Tory Minister Penny Mordaunt told MPs: "We are working tirelessly to get a deal but we cannot accept a deal at any cost. We cannot accept a deal that would compromise the control of our money, our laws, borders and our fish.
"The only deal that is possible is one that is compatible with our sovereignty and takes back control of our laws, trade and waters."
She said the UK would carry on talking "until there is no hope" of a deal, adding: "At the moment there is hope of that happening, even though things do appear gloomy."
But Labour's Rachel Reeves expressed "huge dismay" that progress was not achieved on Wednesday.
The Shadow Chancellor of the Duchy of Lancaster said: "The country was hoping for a breakthrough last night, yet there was none.
"There is a sense of huge dismay as we all wanted to hear significant progress but we heard more about the Prime Minister's meal than we did about his deal."
