Defra says it has no plans to extend the deadline for 2016 Basic Payment Scheme applications beyond 16 May.
Some farmers have called for a deadline extension so they can make an accurate 2016 application following delays to 2015 payments.
But others fear that extending the deadline will have a knock-on effect, delaying 2016 payments – as happened last year.
The European Union has granted permission for member states to extend the application deadline one month to 15 June.
Brussels said it was up to individual countries to decide whether they wanted to take advantage of the concession.
But Defra said English farmers were on track to get their 2016 applications in on time.
“There are no plans to change the deadline, as this could lead to unnecessary delays in payments being made,” said a Defra spokeswoman.
“We urge everyone to complete their application as soon as possible.”
English farmers appear to be making good progress with completing their 2016 Basic Payment Scheme applications, with less than two weeks to go until the deadline.
But progress looks to be slower in Scotland, where only about one-quarter of applications are in so far.
Nearly half of farmers in England had completed their form by 2 May, according to the Rural Payments Agency.
To date, 33,564 people have submitted a claim online, 5,833 completed a paper form and another 14,707 are showing in the online system as “in progress”.
This means about 61.5% of applications have either been submitted or are being worked on by applicants.
At a similar point last year (6 May), just 8,500 applications had reached the RPA, although by then the agency had already extended the deadline into June, so farmers did still have six weeks left.
In 2014, when the deadline was mid-May as usual, 45,000 applications were made online by the end of April.
16 May deadline
In a statement, the RPA urged farmers to complete their application before the deadline of midnight on 16 May, even if they were still waiting to resolve queries on their 2015 application.
All 2016 claims would be automatically updated with any verified changes in 2015 claims, it said.
RPA chief executive Mark Grimshaw said: “We are on track, with figures to date matching this stage in previous years.
“But we are never complacent and hundreds of RPA people are standing by to help farmers get their applications done and in on time.”
Looking forward, the agency said groundwork put in this year means 2016 claims “can be processed and paid earlier in the payment window”.
A spokesman for the Scottish government said to date it had received just under 5,000 applications – online and paper versions – and it expected to receive 20,000-21,000 applications in total.
This was significantly more than had been received by the same date last year, although the deadline was extended to June in 2015.
“Our online application process has generally performed well this year. We would urge farmers not to delay and to get on with making their applications,” the spokesman said.
A spokesman for the Welsh government said it had received about 8,000 of the 16,000-17,000 applications it expected and there was usually a rush of forms in the last two weeks.
Applications were up 12% on the same point as last year, with the online system working well, he added.
Wales did not extend its application deadline in 2015.
In a statement issued on 29 April, the Department of Agriculture and Rural Development (Dard) in Northern Ireland said 6,200 farmers had already applied online, but it wanted more to follow suit.
Dard has said if 70% of claims are made online, it will commit to making advance payments in October 2016.
“If more farmers submit their application online then fewer resources will be required to carry out validation checks, which means resources can be redirected to make more payments earlier to more farmers,” said a Dard spokesman.