I see a pair of twins, boy and girl, in Glasgow Milton in 1953, refs 644.10/191 and 644.10/192.
One of them is William Boyce Hutchison who died in Ayr in 2011, mother's surname Boyce. He is also indexed as William Boyce Shaw.
The other twin seems to have married twice, once in 1972 and again in 1987, and I have not found a death.
However a Catherine Aird Boyce or Hutchison or Shaw died in 2002 aged 74. Catherine Aird Boyce married first in 1949 (have not found this husband's death) and again in 1965 (there are four possible deaths of the second husband but he might still be living.
Obviously, this doesn't match the story of the twins' mother being Helen Boyce, or of the twins being adopted.