The Red Box Project, which campaigned for the scheme to be introduced, said all schools should be taking part to support the one in 10 young people experiencing period poverty.
Department for Education data shows that only 25 of the 61 state-funded schools in North East Lincolnshire ordered free period products for their pupils between the start of the scheme in January 2020 and the end of last year.
Schools can order the products online and they are delivered to them free of charge.
Products they can order include period pads and tampons, and environmentally friendly alternatives such as period cups and reusable pads.
They are available to all pupils who need them, including those who have forgotten products, start their period unexpectedly, or cannot afford them.
The figures show £7,953 was spent in total to provide the products in North East Lincolnshire.
Each participating school spent on average £318, around 57 per cent of the £557 spend cap.
A report published by the DfE said that schools had been less likely to order period products while pupils were learning from home during the pandemic.
Across England, the uptake of the scheme has been around 41% in primary schools, and 76 per cent across secondary schools.
Clegg Bamber, co-founder of The Red Box Project, said: "Whilst primary schools won't have as many pupils menstruating as secondary schools will, there will still be some pupils who will be menstruating and should rightly have access to the period products they need at school.
"Starting your period at any age can be a distressing time, even more so when you are at school, but by having the period products there available to students who need them it takes away some of the pressure and angst of wondering where they are going to be able to find a suitable period product from.
"Government should be striving for 100 per cent take-up across all institutions – primary, secondary and further education – and more has to be done to see those levels increase."
He added that access to period products outside school settings should also be considered.
"Whilst the period products scheme is a great step forward and something we campaigned for, there are limitations.
"Schools are only in attendance for 39 weeks of the year and menstruation cycles do not stop for school holidays and this has to be considered when thinking about the issue of period poverty affecting young people."
A Department for Education spokesman said: “No pupil should ever have to miss school because of their period.
“More than three-quarters of state secondary schools and colleges in England accessed period products using the Government’s scheme during its first year.
“The scheme remained in operation during partial school and college closures, and now that they have returned we expect uptake of the scheme to return to pre-lockdown levels.”