but the title of the SERP link is the anchor of the link, which, in turn is just a part of the URL of the page
Is that what the visible text in the linking page says? Or is the search engine replacing the linking text with the content of the <a href> hiding behind it?
If the page itself just has your raw URL, there's not a whole lot you can do about it. Unless you want to contact the linker and asking them to please replace "see <a href = "http://www.example.com/abc/def/1234.html">www.example.com/abc/def/1234.html</a>" with "see <a href = "http://www.example.com/abc/def/1234.html">the world's leading authority on widgets</a>".