In a speech to a right-wing US think-tank, Mrs Braverman claimed asylum was routinely offfered to people for "simply being gay,or a woman and fearful of discrimination in your country of origin".
Lib Dem council group leader Chrissie Bainbridge and deputy leader Katrina Trott said: "We, Liberal Democrats, abhor the views of the Home Secretary who time after time has shown she has no compassion, zero humanity and a flagrant disregard for the vulnerable and those escaping war, poverty and persecution."
The councillors' joint statement went on: "This comes from a government that cut its overseas aid budget, when climate change with increasingly extreme weather patterns has resulted in famine and conflict that makes refugees of many people from many countries.
"The Tory Government gave millions to Rwanda and France and still hasn’t created safe routes for asylum seekers. It is difficult in many countries to even submit asylum requests. There is currently more immigration from Hong Kong and Ukraine than anywhere else.
"LGBTQ individuals are criminalised in 64 countries across the world, almost half of which are African countries. They face imprisonment, torture and even execution and are desperate to live openly and safely. For Suella Braverman to suggest that 'many people' pretend to be gay in order to seek asylum is completely without evidence.
"We have previously had a proud history in this country of welcoming foreigners to our shores who have contributed to our economy, demonstrating that different cultures can live harmoniously together and integrate well when there is the will and structures to do so.
"Fareham has welcomed refugees from Afghanistan and Ukraine. The borough is home to many people of different faiths and cultures. We believe Suella Braverman's statements, a second generation immigrant herself, to be wholly at odds with reality and demonstrates just how out of touch with the people of this United Kingdom this broken government is."
For a more balanced account of why refugees come here, and how they fit with our society, see: