A scheme to offer pupils free school breakfast and lunch irrespective of income has been launched in an attempt to tackle the growing food poverty crisis in parts of the UK.

Hammersmith and Fulham council rolled out the scheme in west London on Wednesday. It said the national free school meals system was not working, leaving many children going to school hungry and remaining hungry throughout the day.

Officials say the threshold for families to qualify for free school meals is too high and the stigma of being singled out for free food while fellow pupils pay is damaging to both children and their families.

About 750,000 secondary school pupils in the UK are eligible for free school meals, at a cost per student of about £440 a year, but thousands of children with no recourse to public funds who are living in poverty may not be eligible. Others living in poverty are “not poor enough” to qualify.

Free primary school meals are available to all pupils in reception and years one and two. Three London councils – Islington, Southwark and Newham – provide free school lunches to all primary school pupils.

Availability of breakfast clubs at primary schools varies and many charge a fee. There are currently no state secondary schools offering universal free lunches.

A Human Rights Watch report last month said tens of thousands of families did not have enough to eat. Some schools in Oxford have turned to food banks to feed their pupils.

From September, free breakfasts will be universal for all primary school pupils in Hammersmith and Fulham regardless of family income, and from January 2020 the council will be the first in England and Wales to roll out a pilot scheme to deliver free lunches in two secondary schools.

The scheme will be funded from money paid to the council by property developers as one of the conditions for granting planning permission. Around 10,700 children will benefit from the pilot.

Alison Garnham, the chief executive of Child Poverty Action Group, said: “Poverty and hunger exclude children from some learning and social opportunities and leave them exposed to stigma and shame. This pilot recognises the scale of the problem and strives to address it head on.”

Sally Brooks, the headteacher at Fulham college boys’ school, which is involved in the pilot, said its impact on students would be immeasurable. “Providing the boys with a nutritious meal will not only allow them to compete in an academic environment, but will also give them the nutrition needed to go above and beyond what is required of them at school and actively participate in extra-curricular activities.”

The council’s leader, Steve Cowan, said food poverty was a national crisis,. “This initiative is a step forward in the fight to end this blight on our children and their future wellbeing.”

Cowan said he hoped other councils would follow suit.

The Department for Education has announced that about 50,000 disadvantaged children in England will be offered free meals and activities over the summer holidays at a cost of £9.1m. The scheme follows a £2m programme last year that reached 18,000 children.