The tests assess entitlement to employment and support allowance
A letter urging Prime Minister David Cameron to get rid of work assessments for the disabled has been signed by the dean of St Paul's Cathedral.
The letter also called on ministers to address the "shameful offences" of austerity measures.
The government said the assessments had been improved and could help disabled people get into employment.
The letter, titled The Downing Street Demand, called for an end to work capability assessments (WCA) which "demean and distress" disabled people.
It stated that government policies forced some of the most deprived members of society to "shoulder the heaviest burden of national debt created by the super-rich".
The letter to the prime minister said:
"In 2010 you said 'I'm going to make sure no-one is left behind; that we protect the poorest and most vulnerable in our society'.
"The reality of the austerity programme is the opposite.
"Since your government came to power, cuts have meant that disabled people are paying back nine times more than non-disabled people and those with the highest support needs are paying back 19 times more."
'Dignity and security'
The campaigners were particularly critical of work capability assessments, changes to housing benefit - the so-called bedroom tax - and benefits changes including the disability living allowance (DLA) and personal independence payment (PIP).
Work capability assessments were introduced in 2008 to assess entitlement to employment and support allowance (ESA).
"The support needs of complex disabilities and mental health issues cannot be assessed by a tick-box system," the letter continued.
It suggested WCA should be replaced with a "rigorous and safe system that does not cause unavoidable harm".
Dr Ison, who presided over the funeral of Baroness Thatcher, said: "It's right to stand in solidarity with people from many different organisations to draw attention to the needs of some of the most deprived members of our society.
"The government needs to respond by enabling disabled people to live with dignity and security."
Campaigners said 56,000 people had signed a petition supporting an end to the "degrading" assessments.
A Department for Work and Pensions spokesman said: "It is important we don't simply write-off people who have a health condition or disability.
"The old incapacity benefits system condemned too many people to a life on benefits with little hope of moving back to work.
"Now people who can work will be given help to find a job while those who need unconditional support will get it.
"Through a series of independent reviews and by working with medical experts and charities, we have considerably improved the WCA process since 2010 to make it fairer and more accurate.
"The percentage of people entitled to employment and support allowance is now at its highest level with over half of people completing a WCA eligible for the benefit."