Send for a taxi to Mile End (5)

I believe the answer is:

cable

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'send' is the definition.
(send a message by cable)

'taxi to mile end' is the wordplay.
'taxi' becomes 'cab' (synonyms).
'to mile end' becomes 'le' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'cab'+'le'='CABLE'

'for a' is the link.

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(Other definitions for cable that I've seen before include "Telegram; wire rope" , "Conductor for transmitting electric power" , "Communication - wire - 200 yards in length" , "Hawser, wire" , "Rope; message" .)

I've seen this clue in the Evening Standard.

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