The Department for Education provided 200,000 devices to local authorities and school trusts between May and July to help children access remote learning while schools were closed.
But the office of the Children's Commissioner for England (CCO) said the £100 million scheme, aimed at care leavers and pupils with social workers, failed to help hundreds of thousands more children.
Figures obtained by the organisation show Shropshire Council ordered 500 laptops and tablets while Telford & Wrekin Council ordered 502.
Both councils ordered the maximum they were entitled to.
Simone Vibert, senior policy analyst at the CCO, said nine per cent of families in the UK do not have a laptop, desktop or tablet at home – a "digital divide" that became more apparent during the Covid-19 crisis.
She said: “During this pandemic, proper access to the internet is not a luxury for children having to learn at home, it is a necessity.
"The Government needs to ensure that all children are able to access education in the coming weeks and months, hopefully in school, but also remotely if that becomes their only option.”
Though the devices were "very welcome", the Children's Commissioner Office estimated there are 540,000 children in groups eligible for the scheme, meaning many more missed out.
In addition, 20,000 were set aside for disadvantaged Year 10 pupils who were singled out because of concerns they would fall behind in preparing for their GCSEs in the coming school year – with 26 allocated in Telford and Wrekin and 14 in Shropshire Council's area.
But the Children's Commissioner Office said this overlooked the needs of disadvantaged children in every other year group, and even the Government's planned extension of the scheme to Years 3 to 11 may be "insufficient".
Telford and Wrekin was also allocated 78 4G hotspot devices, and 11 for Year 10 students.
Shropshire was given 57 4G devices, and six for Year 10 students.
Turn2us, a charity which helps people living in poverty, said digital skills that help children prepare for adult life are more important than ever following the coronavirus lockdown.
Liam Evans, campaigns officer at Turn2us, said: "It is crucial that more computers are delivered to children who are living without.
"The Government have a moral duty to make sure all kids have an equal opportunity to thrive, and this is core to that."
A Department for Education spokesman said: “For disadvantaged children whose education is disrupted in autumn term, we are initially providing an additional 150,000 laptops and tablets to schools, who will be best placed to pass these on to children who need them.
“Children will be returning to school full time in September and we have invested £1 billion in a Covid Catch Up Fund which will also provide one-on-one and small group tutoring for disadvantaged pupils.”