I haven't had time to search extensively for copies of the
Girls Own Paper 1902-3, but information in the UK press shows that a painting by Alyn Williams of Queen Mary, then Princess of Wales, was used in the November edition for 1902.
November 1902
A painting of Queen Mary by Williams was on display at a London gallery in October 1902.
In March 1895 Queen Mary, as Duchess of York, gave sittings to Alyn Williams.
March 1895
And it would appear that this was the painting on display in London in October 1902.
October 1902
The only painting of Queen Alexandra by Williams I have found reference to so far was done in 1904.
February 1904
As the image below obviously comes from a book, it is possible that it was the one used in Williamson's book mentioned in the cutting above. There are copies of Williamson's book on sites such as Archive.org, but I haven't seen one with the copy of Queen Alexandra's portrait by Alyn Williams.