The equality watchdog has earned cautious approval for its response to recommendations made by a House of Lords committee that examined the impact of the Equality Act on disabled people.

The committee concluded earlier this year that the government was failing to protect disabled people from discrimination, and that there were problems with laws designed to address disability discrimination in “almost every part of society”.

Last week, the disabled crossbench peer Baroness [Jane] Campbell, who was a member of the Equality Act 2010 and disability committee throughout its nine-month inquiry, said she was “bitterly disappointed and angry” with the government’s response to the report, which she said was a “wasted opportunity to kick-start a progressive equality agenda for the UK’s 11 million disabled people”.

This week, the Equality and Human Rights Commission (EHRC) delivered its own response to the report, including eight recommendations that call for it to take action itself.

Of those eight recommendations, it accepted two, but also accepted four more “in principle”, and rejected two.

Although it turned down a call to work with local and national disabled people’s organisations (DPOs) to raise awareness of disabled people’s rights under the Equality Act, it agreed to explore with DPOs an effective way to raise awareness of “rights and responsibilities”.

It also said it would work with DPOs to consider how best to promote the use of reasonable adjustments.

But the commission rejected outright a recommendation to return stronger powers to its disability committee, which is due to have its statutory decision-making powers removed next April, and also declined to work with disabled people and their organisations to co-produce a major “disability-specific action plan”, because it said disability was already “embedded” in its programme of work.

David Isaac, the commission’s new chair, who was appointed by the government, said the report showed that progress on achieving disability rights had “stalled”, and he demanded a new national focus on disability rights so that disabled people were no longer treated as “second class citizens”.

He called on the government to show stronger leadership by introducing the remaining parts of the Equality Act that have yet to be implemented, including those on dual discrimination; access to ships; common areas of rented blocks of flats; access to buses and coaches; and the requirement for political parties to report on the diversity of their candidates.

And he said that service-providers such as restaurants, theatres, concert venues and sports stadia must “raise their game” on access.

He said: “It is a badge of shame for our society that thousands of disabled people are still not being treated as equal citizens and the everyday rights non-disabled people take for granted, such as being able to access transport, housing, restaurants, theatres and sporting events, are still being denied.”

He said EHRC itself must “use its position to bring people together”.

And he pointed to work the commission has already announced it will carry out this year, including helping to prepare a shadow report to the UN committee on the rights of persons with disabilities; investigating the impact of government welfare reforms on disabled people; and launching a major inquiry into disabled people’s housing.

Disability Rights UK (DR UK) welcomed the commission’s commitment to work with disabled people and their organisations, and Isaac’s comments.

A DR UK spokesperson said: “We look forward to working with the commission to ensure that the full participation of disabled people is central to their overall work for a fairer, inclusive Britain.

“However, there is still a huge question about how the commission will be led and steered in its disability work once the disability committee comes to the end of its life in March 2017.

“Also, the commission has accepted some of the House of Lords’ recommendations ‘in principle’ – and we will want to see more clarity about what ‘in principle’ agreement will really mean.

“For instance, how will disabled people be informed of their rights in practice?”

Disabled campaigner Doug Paulley, who gave evidence to the committee about how the system failed to protect disabled people from discrimination, said he was pleasantly surprised at how well the commission had engaged with the committee’s recommendations.

He has previously been critical of the commission, which he believes has been left “ineffective and rudderless”, but he said it had “engaged with the issues in detail and with some thought”.

He said: “Doubtless it will continue to largely not use the powers afforded to it; doubtless too it is underpowered by the government’s failure to behave responsibly or reasonably, and by limited resources.

“But I think there is at least some hope, some potential shown in the report, that they could start to change some elements of their ethos and operation.”

Baroness Deech, who chaired the committee, said she found the commission’s response “really quite positive” and said that it was a “platform to build on” and showed a “spirit of willing to get on with this”, while it was “definitely more positive than the government’s”.

She said there would be a House of Lords debate on the committee’s report in early September, and promised that she and her committee colleagues would “certainly be standing up as individuals for more action”.

Baroness Deech also said she hoped that she could persuade the new minister for women and equalities, Justine Greening – who replaced the sacked Nicky Morgan, who was responsible for the government’s response – to “look again” at the report’s findings.