Nissan aims to optimize its investments in Europe by consolidating X-Trail production in Kyushu, the production hub for the global model, the company added.
The newspaper said that Greg Clark, the business secretary, was told by the vehicle giant that the switch of production from Sunderland to Japan was now "not negotiable".
Nissan had been making the cars in sunderland since 1986 and it has nearly 7,000 people employed there.
In the 2016 letter from Mr Clark to Nissan's then chief executive Carlos Ghosn, he said the funding was contingent "on a positive decision by the Nissan board to allocate production of the Qashqai and X-Trail models to the Sunderland plant".
She said: "Of course Brexit was not the only reason but it was pretty prominent in Nissan's decision".
The decision not to build the SUV in Sunderland, which employs more than 7,000 people and supports another 28,000 supplier jobs, is a blow after Prime Minister Theresa May's government had previously gone out on a limb to safeguard Nissan's investment in the UK.
Bush said: "Unite will continue to press for further long-term guarantees over future investment and new models to secure the site's future for generations to come".
Meanwhile, pro-EU and pro-Brexit U.K. politicians traded allegations about whether Nissan's decision not to build a new SUV in northern England was the latest Brexit-induced damage to Britain's economy.
Nissan Motor on January 2 said it would use a plant in Kyushu, Japan to build the next generation of its X-Trail sports utility vehicles for the European market. Over the last few weeks we have seen similar moves from a string of vehicle makers and large businesses, especially with regard to continued free movement of components within the same industries.
Clark said in the 2016 letter that government had already been able to confirm £22m of support for the foundry at Sunderland to become a European development centre for the firm's alliance with fellow carmakers Renault and Mitsubishi.
"From a Brexit perspective, the one thing it highlights is the uncertainty".
In addition, Gianluca de Ficchy added that uncertainty over Brexit has not helped the firm "plan for the future".
"What we should have been saying to Nissan was thank you", he said.
In contrast, the company is pressing ahead with its other investments in Sunderland, including the next-generation Juke and Qashqai, and its best-selling electric auto, the Leaf.