A government order means poultry must be kept indoors until the end of February or kept away from wild birds.
The H5N8 bird flu strain has been found in poultry in Lancashire, Lincolnshire, Carmarthenshire and North Yorkshire.
Under current EU rules, products from poultry housed for less than 12 weeks can be still marketed as free-range.
This 12-week allowance for birds housed owing to avian flu will come to an end on 28 February.
The rules also affects products which contain free-range egg, such as mayonnaise.
Daniel Winter runs Trinity Farm in Nottinghamshire, where he keeps a small flock of about 100 free-range hens.
He needed to build a new covered enclosure for them, costing Â£1,000.
"If it should continue for months, then we'll end up losing the free-range label," he said.
His business is trying to avoid putting up the price of their eggs.
"We've been swallowing the cost, hoping it would end, but at some point, we are going to have to start looking at passing the cost on," he said.
Ruth Mason, chief food chain adviser at the NFU, said: "Plans need to be put in place in terms of how eggs can be marketed and how they should be positioned.
"It is very logistically difficult for the industry to move overnight from calling one product free-range to calling it 'barn' or whatever that might be.
"We may well get to a place where we have a free-range packaging that has a sticker over it that explains the birds have been housed, so it may say 'free-range, however, birds are currently housed due to avian influenza'."
Barn eggs are traditionally cheaper in the shops than free-range eggs.
A spokesman for the Department for Environment, Food and Rural Affairs (Defra) said: "We have taken swift action to limit the spread of the disease, with restrictions around affected premises and wider measures in place across the country, including a legal requirement for all poultry keepers to keep their birds housed or otherwise separate from wild birds. This must be coupled with good bio-security.
"All measures will be kept under review based on the best available evidence, and we are working closely with the industry on next steps."
Similar restrictions have been introduced in Scotland, Wales, and Northern Ireland.
You can hear more on this story on BBC Radio 4's You and Yours

Under the new rules, households will be fined $1 (Â£0.61) if their rubbish bins contain more than 10% food waste, and businesses and apartment buildings $50.
The city already recycles 56% of its waste but is aiming for 60% by 2015.
Seattle, in Washington State, is the second US city after San Francisco to make composting mandatory in an effort to reduce greenhouse gas emissions.
Composting is the processing of breaking down food and lawn refuse into useable soil through decomposition.
Up to 40% of food in the US is wasted, according to a report by the Natural Resources Defense Council.
Only 5% of food scraps are composted, according to the US Environmental Protection Agency (EPA).
Many Seattle homes and businesses have food compost bins but are not required to use them - now they will have to.
The city will begin issuing warning tickets on 1 January 2015 and fining customers on 1 July, according to the ordinance, which passed unanimously on Monday.
Under the new rules when Seattle garbage pickers see too much food waste in a rubbish bin, they will note it in a computerised system and the fine will be added to the customer's rubbish carting bill, local media reported.
Multi-unit flats and businesses will also be required to limit their food waste but will get two warnings before they are fined, according to the Seattle Times newspaper.
Seattle officials do not expect the programme to be a money-maker for the city, Tim Croll, the Seattle Public Utilities solid waste director, told the newspaper.
He added the city has collected less than $2,000 (Â£1,220) over nine years of a similar programme that banned recyclable items from the rubbish.
"The point isn't to raise revenue," Mr Croll said. "We care more about reminding people to separate their materials."
Correction 10 October 2014: This report has been amended to clarify that fines will apply for disposing of food waste incorrectly rather than doing so at all.
The National Farmers' Union is calling for clarity on what will happen to free-range labelling if restrictions owing to avian flu continue.
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The Seattle city council has voted to fine businesses and residents that do not recycle their food waste.