A number of people were also injured in the blaze at Grenfell Tower and the fire service are continuing to carry out their investigations.
SDLP MLA Nichola Mallon expressed her sympathies and said: "My thoughts and prayers are with the residents of Grenfell at this horrendous time. As the death toll continues to increase and more tragic stories of loss emerge, our deepest sympathies are with those who were injured or lost their lives.
I have been in touch with the Housing Executive and I'm pleased that they are planning a review across their 32 tower blocks. This should include a full assessment of new cladding attached to individual blocks in areas like the New Lodge in North Belfast as well as a review of fire safety procedures.
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"The reports of poor fire alarm coverage and single stairwell escape routes from Grenfell are terrifying. No one should even have to imagine those circumstances.
"I would also urge everyone to spend time with their families discussing what happens in the event of a fire. These emergencies can happen at any time and don't just affect tower blocks. Everyone should be prepared in case the unthinkable happens."
Sinn Féin MLA Carál Ní Chuilín said: "I welcome the news that the Housing Executive is set to carry out urgent inspections of all social housing tower blocks following the Grenfell fire tragedy in London.
"I wrote to the Housing Executive to seek clarification on procedures for emergency evacuation for residents living in tower blocks.
"I also raised the concerns of several residents from the seven towers in the New Lodge about the use of cladding on the tower blocks and I am reassured the Housing Executive has stated it will take on board any relevant findings of the investigation into the Grenfell Tower fire.
"I would urge the Housing Executive and the Fire and Rescue Service to continue to carry out regular health and safety checks on the tower blocks."
(CD/LM)
