Ms Harman said the government was committed to equality
Councils would have a duty to consider older people's needs and avoid using "complicated technology" in providing services, under government plans.
The Equalities Bill unveiled in the Queen's Speech aims to end age discrimination "in the provision of goods, facilities and services".
Public bodies would have to consider how services affect gay and transsexual people, old or religious people.
They already have to consider effects according to race, disability and sex.
The bill, which covers Britain, replaces nine laws and 100 different rules and aims to strengthen discrimination legislation.
It also includes a ban on wage secrecy clauses in contracts, which forbid colleagues from discussing their pay - in an effort to tackle the pay gap between men and women.
Under proposals in the bill, public bodies would have to report on any pay inequalities and the Equality and Human Rights Commission would start a series of inquiries into pay - starting with the financial sector.
On age discrimination the bill says things that benefit old people, like free bus passes, would still be allowed.
And it says public bodies "will also have a new legal duty to tackle age discrimination and take older people into consideration when planning services, such as not providing car parking tickets through complicated technology which older people may be less able to use".
It would extend the existing duty on public sector bodies, like councils, to consider how their "spending decisions, employment practices and service delivery" can affect people according to race, sex or disability to cover "sexual orientation, gender reassignment, age and religion or belief".
'Hold society back'
As examples the government suggests more park benches so old people can enjoy public spaces and more drop-down kerbs to help people in wheelchairs.
Positive action on employing staff will be "entirely optional" under the bill and is "not about quotas".
But bosses who wanted to positively discriminate would have to ensure the candidates were "equally suitable" and there was evidence that a group - for example women or ethnic minorities - were underrepresented.
Equalities Minister Harriet Harman said: "This government is unconditionally committed to equality. We're not going to put it on the back burner just because times are difficult.
"Fairness and equality are enduring principles of basic human dignity, and fairness doesn't cost anything."
She said equality was needed to avoid resentment among communities and to create a society "which is at ease with itself".
Amanda Ariss, of the campaign group the Equality and Diversity Forum, said she was "delighted" at the bill adding: "Discrimination and inequality blight individuals' lives and hold our economy and society back.
"At a time of recession it is especially important that we make full use of the talents of everyone in Britain and enable everyone to contribute to our society."