According to the Royal Collection site, these buckles may have originated with Augusta, Duchess of Cambridge, a sister-in-law of William IV and grandmother of Queen Mary. The Royal Collection site also notes that the "buckles" have mounts for a bracelet on the reverse.
Although the Royal Collection site does not say outright that the buckles entered the collection through Queen Mary, that is one possible deduction from what the site does say.
The will of Augusta, Duchess of Cambridge sadly for us does not say anything about her jewels at all. Presumably most were divided among her three children prior to her death, or she left other directions for their eventual dispersal.
Her second daughter, Princess Mary Adelaide of Cambridge, Duchess of Teck, died intestate, so we have no precise knowledge of how individual items were shared between her children, although some individual items can be traced (from photos) among her children.
Highly probable provenance of these "buckles".
In her will Princess Sophia Matilda, daughter of the first Duke of Gloucester and Edinburgh and Maria Walpole, Duchess of Gloucester and Edinburgh, left three bracelets to Princess Mary of Cambridge, as she was then called. The latter is perhaps better known to us as Princess Mary Adelaide, Duchess of Teck, mother of Queen Mary.
Princess Sophia Matilda
The first mentioned bracelets were described by Princess Sophia Matilda as --
"my wide gold bracelets having the cyphers of King William IV & Queen Adelaide in diamonds on the blue enamel clasps..."
Then the Princess described another bracelet as
"a single [armlet] of blue enamel & having the portrait of Queen Adelaide surrounded with diamonds for a clasp..."
The will described these bracelets as having been the gift of William IV.
I strongly suspect that the bracelet with the portrait of Queen Adelaide mentioned in the will of Princess Sophia Matilda is this one, now in the Royal Collection.
The Royal Collection notes that this bracelet was purchased by Queen Mary from her brother, Adolphus, Marquess of Cambridge in March 1919.
Given that, I think that it is highly likely that the jewel had originally belonged to his mother, and is highly likely to be the one Princess Sophia Matilda left to Mary Adelaide, later Duchess of Teck.
Even though I have no direct evidence from sources like the jewel inventory of Mary Adelaide, Duchess of Teck to verify that she owned the three bracelets, it seems too much of a coincidence that she was left 3 bracelets matching the description of these bracelets which the Royal Collection describes as having belonged to members of the Duchess of Teck's family. It seems to me highly probable that the bracelet with the portrait of Queen Adelaide for a clasp and the two "buckles" with the cyphers of William IV and Queen Adelaide were the jewels left to Mary Adelaide by Princess Sophia Matilda.