The group said that it expects to have reopened 281 of its stores by that date, having already reopened 112 of its sites across mainland Europe.
The retailer said it is awaiting further guidance regarding stores in Scotland, Northern Ireland and Wales but anticipates openings in “late June”. ABF shut all its Primark stores in March in the face of the virus.
ABF, which also owns a large food business, has been losing £650 million in sales for every month that all stores were closed, with no online trading to fall back on. It said that it cut more than 50 per cent off overheads at Primark in a bid to stabilise its finances during the pandemic.
In a statement, the company said: "As European governments have begun to ease restrictions on clothing retailing we have been able to reopen stores.
"Safety has been our highest priority in our detailed preparations to welcome our customers and employees back to stores. We are following government safety advice in all markets.
"Importantly, we will apply the valuable experience gained from more than 100 stores which are already open as we open the remainder of our estate, including stores across the UK.
"Social distancing protocols, hand sanitiser stations, perspex screens at tills and additional cleaning of high frequency touch points in the store are among the measures we are implementing."
Shore Capital analysts said: “With respect to Primark, ABF has set out quite detailed information although the coronavirus crisis remains something of a moving target and, as such, forecasting is challenging.
“Shopping patterns are changing, with social distancing requirements necessarily adjusting previous patterns; so Primark is seeing some shifting in the timing of shopping, a flattening through the week, and larger basket sizes.
“The one key question to us for Primark from this recent experience is whether or not it leads to an adjustment in its online strategy; where partnerships maybe be a worthwhile move, especially if full and partial lockdowns are part of future life; Primark's store only model in this respect has been a strategic challenge.”
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