Barbara doesn't own it, and Barbara doesn't think she owns it. Barbara is a chancer, hoping to make a claim based on (from the 1st post of thread 1):
-the previous owner (a “very dear friend” of hers apparently) let her use it
-she’s been using it for 10 years
-she’s cultivated this patch for several years
-she grows all her veggies here
-it’s her sanctuary
-she paid for the shed
She doesn't think the previous owner gave it to her (even if she thought that, it's clear that hasn't been done in any official way). She knew the house and plot were sold. She planted things anyway in a land grab attempt.
The OP has very wisely instructed a solicitor to deal with it and made a record of the current condition of the plot.