There's a whole world of technicalities involved in calculating the figures - the increase could also be partly attributable to the fact that there were no definitive records kept prior to the pandemic. There was no centralised database - the Local Government Association estimated the number before Covid as being 250,000, far in excess of the amount she is quoting, but also said that it could be far higher.
The attempts to quantify the true number will have involved healthcare records, child benefit claims, birth registrations, local authorities having to investigate and trace parental financial transactions and passport use, trying to get private schools to participate, hoping that EHE parents agree to notify their LA (which they are not required to do and plenty refuse), getting school staff who may not have any experience and nobody to show them how to use the archaic technology that serves as notification, LA staff who may not know how the multiple systems work - and there is also the added complication that this can be used as a political tool (such as the thinktank she is using for her article).
In short, nobody knows how many children there are in the UK and nobody knows how many were missing before or how many are missing now. And then reason why? Because when it was previously tried, it was abandoned as being too huge a task to retrospectively introduce.
However, it is not being ignored. There's huge amounts of work being done to try and create records and monitor things in real time. But it takes huge amounts of time for even the children they know exist - a single referral takes around 2 hours to process before it's even submitted. The hours involved for a caseworker dealing with one child is ridiculous. There isn't the funding, the hours in the day, willingness, technology or capacity on the part of some schools, the infrastructure to do it - but they're expected to try and make a Herculean task work with a few spreadsheets, email and assorted archaic portals.
She writes very emotively. None of that addresses the fact that money is needed. Real money - not just for IT, but for the many thousands of hours' work this entails, starting right at the point of being able to afford the salaries of people to do the work.