The company is asking workers to travel to sites and pick clothes for online orders "to keep the company operating", according to a letter sent to employees on Tuesday evening.
But worried staff have questioned whether picking clothes is an "essential" job at the same time the Government has called for all non-essential workers to avoid unnecessary travel.
Prime Minister Boris Johnson said on Monday night that the public "must stay at home" unless they work in a key sector or industry.
But retailers can still trade online, and the Government is now under pressure to intervene to end the confusion about which businesses can continue to operate.
The letter to Next staff said: "We need to keep the online business functioning to be certain that Next emerges from this short term crisis.
"To help us, we are looking for a small number of staff to attend work to pick and process the stock in our stores that customers have purchased online and keep the online business going. We will only look to achieve this on a voluntary basis."
Bosses also laid out a series of measures to ensure social distancing and a clean work space, including limits on the number of people in each store and rules that items are only touched by one person.
The letter added: "We fully understand that many of you have great concerns about attending work. Please let me reassure you that we are in no circumstances going to ask anyone who is unsure about coming to work to do so.
"We desperately need your support to keep the company operating and we hugely appreciate your help in this.
"If there are any reasons why you personally feel that it is not appropriate for you to work, we will be understanding. For example if you are caring for a vulnerable person at your home, if you cannot manage your childcare, if you cannot travel safely to work, or any other reason."
The letter concluded: "To show our appreciation, if you attend work you will be paid an additional 20 per cent of your basic rate of pay for all hours worked until Saturday, April 11."
Up until last week, Next was telling staff on its internal systems that the retailer considered its "operations as essential" and Next chief executive and Conservative peer Simon Wolfson said he wanted the Government to step up its efforts to support workers and warned of a hit to the non-food sector not seen since the 1973 oil crisis.
A spokesman for Next said: "A very small number of staff at any one time are required to help with online orders.
"This will enable social distancing whilst these tasks are performed."
He also emphasised the new arrangements are completely voluntary and no-one is under any obligation to turn up to work.
On the group's essential status, he added: "The Government has now told us otherwise and before it did, Next had already closed all its stores."