Street some drivers cross over on the way back with wagons (7)

I believe the answer is:

oxcarts

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'wagons' is the definition.
(oxcart is a kind of wagon)

'street some drivers cross over on the way back' is the wordplay.
'street' becomes 'st'.
'some drivers' becomes 'rac' (I've seen this in other clues).
'cross' becomes 'x'.
'over on the way' becomes 'o' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'back' says the letters should be written in reverse.
'st'+'rac'+'x'+'o'='stracxo'
'stracxo' backwards is 'OXCARTS'.

'with' acts as a link.

Can you help me to learn more?

I've seen this clue in The Independent.

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