Disabled people have spoken of their horror, shock and anger at learning of the vote to leave the European Union in last week’s referendum.

Although many disabled people voted for Brexit, the vast majority of leading disabled activists were strongly in favour of remaining in the European Union.

One disabled campaigner, who asked not to be named, said: “I think the majority of disability rights campaigners are in or recovering from shock.

“There was a very strong campaign showing the benefits of EU membership to disability rights, but now that we have left the EU we know very little about what will happen next.

“It feels like the carpet has been pulled out from underneath us and we’re not sure whether the bare boards we’re now looking at are stable.”

In a blog for Disability Now, John Evans, one of the founders of the UK independent living movement, said the day of the referendum would “go down as the blackest day in the modern history for disabled people in the UK and for our human rights”.

He said he was “dismayed, horrified and heartbroken about the consequences facing us and it is hard knowing which way to turn”.

Miro Griffiths, a former project officer for the European Network on Independent Living (ENIL) and now a lecturer, researcher and teacher, said the vote meant that the connection between disabled people in the UK, their European supporters, policies “that reflect the aspirations of the independent living movement”, and “decision makers that would collaborate with us” had been “severely damaged – possibly beyond repair”.

He said: “Disabled people in the UK will become further marginalised as the state begins to dismantle social justice frameworks and destroy the support systems that – currently – do not meet the needs of those who require them.

“The most startling factor to consider is that the majority of those who voted unwittingly accepted this.”

But Rick Burgess, of Manchester Disabled People Against Cuts, said: “I think it’s important not to let the fear and panic the media and politicians are spreading distract us from the fight that is the same today as it was before: to reclaim and reinforce our human rights.

“That struggle is probably going to be harder now, so we have to both increase our resolve and to make sure we look after one another.

“Our advantage is we have been fighting for many years already, we are seasoned and experienced survivors, we are ahead of many non-disabled people who are only now just waking up to the threat from the far right.”

The disabled crossbench peer Lord Low told fellow members of the House of Lords that there was a strong case for a second referendum, as called for in a petition on parliament’s website that by last night (Wednesday) had secured more than four million signatures.

He said he believed the “leave” campaign had won the vote on what was “an essentially fraudulent prospectus”.

He said: “They said that we could continue to trade with the EU on very similar terms without having to accept freedom of movement.

“They said that there would be no adverse economic consequences, but we are already beginning to see them.

“They made completely unrealistic promises as to what could be done with the resources saved from our EU contribution, and, most glaringly of all, with breath-taking cynicism and within hours of victory they were maintaining that they never said that Brexit would enable them to reduce the level of immigration.”

The referendum result drew immediate support for disabled people in the UK from the two main Europe-wide disabled people’s organisations, the European Disability Forum (EDF) and ENIL.

ENIL said it felt “sadness, disbelief and dejection” at the vote, emotions which it said were shared with the UK independent living and disability rights movements.

It said: “We are deeply concerned about the prospect of disabled people in Britain being worse off and hit by further cuts.

“Although discrimination and inequality affect many disabled people throughout Europe, there are numerous EU initiatives that have had a positive impact on our lives and have created a stronger legal basis to protect our rights.”

It said it would “not leave our British disabled brothers and sisters behind and will do everything in our power to support them in their fight for independent living”.

It added: “ENIL respects the democratic right of the British people to decide on their EU membership.

“However, we are adamant that a strong human rights agenda throughout Europe is better achieved together.

“ENIL will continue and intensify its collaboration with disabled people in the UK.”

EDF said it accepted the result of the referendum with “regret”, and also promised to continue to work with disabled people’s organisations in the UK.

Yannis Vardakastanis, EDF’s president, said: “EDF will continue to promote unity and solidarity within the disability movement all across Europe and will work very decisively on our common values against Euroscepticism, xenophobia, racism and all kinds of discrimination.

“From this, we won’t exclude any people with disabilities or their organisations because of political choices.

“We will collaborate with all organisations of persons with disabilities in Europe, including the UK, to ensure that Europe does not lose sight of the importance of human rights of all of its people: women, men, children, older people, persons with disabilities and people on the move across Europe and on our borders.”