There are calls for Britain to be added to Ireland's mandatory hotel quarantine list.
The UK intends lifting almost all restrictions on July 19th - which the British government says could lead to a spike in infections.
The country's Health Minister Sajid Javid says infections could rise to more than 100,000 cases a day in August.
While the latest tracing figures from there suggest an average of about three close contacts are being identified for every confirmed case.
Passengers travelling from Britain to Ireland must have a negative pre-departure PCR test taken within 72 hours before arrival.
There is also a legal requirement to quarantine at home for 14 days.
While travellers can get a second PCR test no less than five days after arrival and, if negative, can end their period of quarantine.
All arrivals must also complete a Passenger Locator Form.
But Independent TD Joan Collins is calling for mandatory hotel quarantine to be extended to British tourists.
She says England's plan to re-open on July 19th poses a big threat to Ireland.
"My concern is that with the Delta [variant] running rampant, the UK could become a variant petri dish, it could become a variant factory.
"We could have mutations developing through how Delta is running through the population.
"And we have to protect our vaccination programme here.
"So I think there has to be a serious discussion with NPHET and the HSE whether mandatory hotel quarantine is put in place."
She says the so-called 'Freedom Day' plan there has changed things.
"There's been a quantitative change now, with this July 19th 'Freedom Day', as Boris Johnson is calling it.
"86% to date have received their first jab in the UK, 64% have received their second dose.
"All adults won't be fully vaccinated until mid-September, that's the timeline.
"They expect to have 50,000 cases by July 19th, and it be as high as 100,000 cases later in the summer".
On Tuesday, Tánaiste Leo Varadkar said the UK's re-opening plan was 'too risky' and warned it could have a spill-over effect here.
"What was announced in England yesterday, in my view, was too risky", he said.
"The prospect of packed theatres in the West End and nightclubs in Manchester being packed to the rafters is one that would concern us quite frankly here in this country because if things go wrong in England it will have spillover effects in Ireland and on the other neighbours."