Futile hope to be taken by tube about a mile (4,5)
I believe the answer is:
pipe dream
'futile hope' is the definition.
(I've seen this before)
'taken by tube about a mile' is the wordplay.
'taken by tube' becomes 'piped' (I can't explain this - if you can you should give a lot more credence to this answer).
'about' becomes 're' ('re' means regarding or about).
'mile' becomes 'm' (common abbreviation).
'piped'+'re'+'a'+'m'='PIPE-DREAM'
'to be' acts as a link.
Can you help me to learn more?
(Other definitions for pipe dream that I've seen before include "Fanciful or impossible plan" , "Fanciful hope" , "Unattainable hope" , "Fantasy" , "Sherlock's flight of fancy" .)