I don't think you should walk away...
Contact the university and find out if they use 'turnitin'. If they do, I would then suggest you contact the student's tutor, explain the situation and ask them to run the version you sent the student and the final version that the student submitted through the system. If you were feeling nice, you could let the student know in advance that you will be doing this, giving them a little time to pay you if they get scared/realise you're not going to let them get away with it. Unfortunately, the student may have completed their course by now anyway and it may not make any difference, but it would possibly help if you then decide to take the copyright approach.
I got the following response from the copyright enquiries team and depending on how heavily you edited it, you may be able to pursue this angle or at least follow the small claims option.
"Thank you for your recent enquiry. Although we are unable to provide legal advice on specific cases, I hope the following general information is of use to you.
Currently, there is nothing in the Copyright, Designs and Patents Act 1988 which relates specifically to proof reading.
However, if you provide services for someone and receive no payment for the work you have done, this may be classed as a breach of contract. Such cases may be pursued through the small claims track, details of which can be found at the following link http://www.direct.gov.uk/en/MoneyTaxAnd ... /DG_195812
It is possible that you could claim some copyright in the work but your input would need to need to be original and of sufficient substantiality as explained here http://www.ipo.gov.uk/types/copy/c-appl ... iginal.htm