One woman says she cannot understand why the Government has not closed the Irish border.
A travel ban from the UK has been extended until the end of the year, as part of new COVID-19 restrictions to take effect from Christmas Eve.
It comes as cases of a new coronavirus strain have been spreading rapidly in Britain.
The mutation - known as VUI-202012/01 - is said to be up to 70% more infectious than the original strain because it has a much bigger viral load.
This has led to a travel ban from several countries - including Ireland - to and from the UK.
However there are no travel restrictions in place between Britain and Northern Ireland - with concerns people can then take trains and buses from Belfast to Dublin and other places.
Julie has three children who live in London.
She told Lunchtime Live that people are making sacrifices, while others exploit the loophole.
"My children were all coming home for Christmas, and then we made the decision a couple of weeks ago that they weren't going to do it.
"Then they were all going to travel to my son's partner's mother's house for Christmas Day so they could all be together with their new grandchild - and now the restrictions in London mean that can't happen either".
She said her son, Paddy, has the coronavirus for the second time and is in isolation.
She said she cannot understand why the Irish border remains open.
"I'm just furious that the Government has not closed the border here.
"I keep hearing about people who have bypassed the travel ban by going to Belfast and then coming down.
"And it's so wrong... we've all made sacrifices".
"People have boasted that they've managed to get tickets to Belfast - they've flown to Belfast and then they're travelling down to the south of Ireland.
"The Taoiseach and his lovely words are all well and good, but he hasn't done what's needed to be done".
While Professor of Experimental Immunology at Trinity College Dublin (TCD) Kingston Mills told The Hard Shoulder on Monday that it will be 'virtually impossible' to keep the new strain out of this country if it reaches Northern Ireland.
"If people don't isolate when they come back from travel, especially from the UK, I know we've got this temporary ban now in place - but obviously people will have come in already.
"And if they haven't got themselves isolated before they get themselves tested and shown to be negative, then they're at a risk of transmitting it to the rest of the country".
He said it is going to be "very hard" to keep it out of Northern Ireland.
"There are more flights going into then North from the UK mainland than there is from the UK to Ireland.
"So it is going to be virtually impossible to keep it out of Southern Ireland if it gets into the North".