I confirm that Ordnance Survey does not hold the information you have requested.
However, under the duty to provide information and assistance in accordance with section 16 of FOIA, we can provide the following which may assist you further in this matter.
It is our understanding this is the article referred to in your request: Where Is The Centre Of Great Britain? | Blog (ordnancesurvey.co.uk)
This article dates back to 2014, at that time, we maintained two datasets, one at 1:250,000 and another at 1:625,000, these datasets were made available as data in Strategi (250k) and GB (625K). Both were retired and withdrawn, with the GB dataset being the first to go several years before Strategi which was withdrawn in 2016.
We do not therefore hold a record of the list of 401 islands which were used to define GB for the purposes of the article in 2014 or the GB dataset, which was the one most likely used.
Using the OpenData Product Strategi and OS Open Names we have been able to compile a list of names for the 400 largest islands based on the coastline length (attached csv file) and also an A3 map (attached pdf) showing their locations which you may find useful. Note no updates have been made to Strategi since 2016. Please be aware, the list we have provided in response to your request, may not be representative of the list used for the purposes of the blog in 2014 and we are unable to guarantee the accuracy of the information provided.
The information supplied to you continues to be protected by copyright. You are free to use if for your own purposes, including private study and non-commercial research, and for any other purpose authorised by an exception in current copyright law. Documents (except photographs) can be used in the UK without requiring permission for the purposes of news reporting. Any other reuse, for example commercial publication, would require the permission of the copyright holder. Most documents supplied by Ordnance Survey will have been produced within government and will be Crown copyright.
In addition, please note that this data is available to download for free on the OS DataHub (Free OS OpenData Map Downloads | Free Vector & Raster Map Data | OS Data Hub) as Opendata, in the form of Strategi Product and the OS OpenNames Product. By using the DataHub and downloading QGIS it possible for you to carry out your own analysis of our data. Therefore, future requests where we consider the information to be reasonably accessible to you as the applicant, are likely to be considered exempt information under section 21 of the FOIA (Information accessible by other means).