Several Yorkshire MPs have already paid tribute to Mr Brokenshire, with Chancellor and Richmond MP Rishi Sunak describing him as "a man of public service and the highest integrity".
Mr Brokenshire, the Conservative MP for Old Bexley and Sidcup, died on Thursday evening with his family at his bedside, and had been in hospital since Sunday.
In September, Mr Brokenshire confirmed his lung cancer had “progressed” and he was starting a new line of treatment.
A family statement on Friday morning said his condition had rapidly deteriorated.
His family said: “It is with deep sadness that we announce the death of James Brokenshire MP at the age of 53.
“James died peacefully at Darent Valley Hospital yesterday evening with family members by his bedside. He had been in hospital since Sunday after his condition rapidly deteriorated.
“James was not only a brilliant Government minister as both Security and Immigration Minister at the Home Office and Secretary of State at the Northern Ireland Office and Ministry for Housing, Communities & Local Government, but a dedicated constituency MP, first for Hornchurch from 2005 to 2010, and then for Old Bexley & Sidcup for the past 11 years.
“But most importantly, he was a loving father to his three children, a devoted husband to Cathy and a faithful friend to so many.
“We would like to thank all the NHS staff, particularly those at Guy’s & St Thomas’ in London, who cared for James with such warmth, diligence and professionalism over the past three-and-a-half years.
“We would also ask that our privacy as a family is respected at this time.”
Mr Brokenshire resigned as security minister in July after telling Boris Johnson that his recovery from lung cancer surgery in February was taking “longer than expected”.
The Prime Minister said he was “desperately sad” to hear the news.
He said in a post on Twitter: “He served with particular distinction in the Home Office and as Security Minister. If the government needed something done well and speedily – and sensibly explained – James was the man to do it.
“I worked with him for many years in London and I know how much he cared for the interests of his Bexley constituents.
“His fight against cancer was heroic, and it is a measure of his resolve that he came back from a first bout with the disease to serve in government again. He will be missed by all who knew him. Our thoughts are with Cathy and his family.”
Chancellor Rishi Sunak wrote: “James Brokenshire was a man of public service and the highest integrity. He was a valued friend and colleague and will be deeply missed.
“My thoughts are with his family on this incredibly sad day.”
Haltemprice and Howden MP and former Cabinet minister David Davis said: "Really sad news about the death of James Brokenshire. He was a very good minister, but more importantly a really decent man. My condolences to his wife and family."
Stuart Andrew, Conservative MP for Pudsey, Horsforth & Aireborough, said: "I am so deeply saddened to hear of the passing of James Brokenshire. A wonderful colleague, I had the pleasure of working with James on a number of occasions. He was unfailingly the most charming, kind, and generous of individuals. My thoughts are with his whole family."
Skipton and Ripon MP Julian Smith, another former Cabinet minister, said: "This is such sad news. James Brokenshire was a man of the highest integrity. A team player, a sensible, moderate voice during the Brexit years - he retained and projected constant humility and empathy during his many successful political roles."
Former Prime Minister David Cameron said: "Devastated to hear the heartbreaking news that James Brokenshire has died, well before his time. He was a hard working and dedicated MP but, more than that, he was a thoroughly decent and lovely man, and devoted to his family. My thoughts and prayers are with them all today."
Labour leader Keir Starmer said: "James Brokenshire was a thoroughly decent man, dedicated and effective in all briefs he held. He fought his illness with dignity and bravery. I’m incredibly sad to learn of his death and send my condolences to his wife and children."
Labour deputy leader Angela Rayner tweeted: “Sending my deepest condolences to the family, friends and loved ones of James Brokenshire.
“He has been taken far too young, a real tragedy. James was unfailingly professional and kind and it was clear that he cared deeply about his work and public service. Rest in peace James.”
Barnsley East MP Stephanie Peacock said: "This is dreadful news. My thoughts are with James’ loved ones at this awful time."
Hull North MP Diana Johnson said: "This is terribly sad news. I shadowed James for several years in the Home Office and he was always incredibly well-prepared, courteous, decent and straightforward to deal with. This is a real loss to Parliament. My thoughts and condolences with his family and friends. RIP."
Rotherham MP Sarah Champion said: "Deeply sad about this, James was a kind and decent man who really cared. I’ll always be grateful for the support he gave to me. My thoughts go to his family RIP."
East Hull MP Karl Turner said: "I was first elected to Parliament in the same election in 2010 as James Brokenshire and knew him from then on. He was a gentleman and was completely committed to public service. My deepest condolences to his family and friends and his colleagues."
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