Ann, in your position I would contact the art student and simply ask for a one-time permission to use the artwork on any and all publications of your book. The artist might be willing to allow that if his/her name is featured, since that could be an opening to future sales of artwork/book covers. You might get a "no" if the artist imagines he/she is losing money, but wouldn't hurt to ask. But get it in writing.
Copyright laws can differ in different countries. US law is not necessarily the same as in the UK (or EU). You might want to check out:
Copyright law of the United Kingdom http://en.wikipedia.org/wiki/Copyrig...United_Kingdom
Australia http://booksat.scarlettrugers.com/bo...my-book-cover/
You can always get in touch with the official guild/union for UK artists and ask for a copy of the copyright rules. There is no charge for this.
But contracted agreements overrule copyright and if you get a signed agreement from the artist, you are free to use the artwork as your book cover. You have already paid for student art, your request is limited to a single book, the copyright remains with the artist, and (statistically) you will not be making a ton of money on your book.
For these reasons it is not improbable that the art student (or perhaps the artist, no longer student) would regard this as an opportunity to get exposure and possibly a new market niche. Or not. Anyway, it costs nothing to ask.
In a similar vein I'll just add that I recently asked permission to translate work of a Swedish poet, and his estate immediately joined a watchdog organization that guards against unauthorized reproduction of literary works and referred me to them for all future contact. I suppose they had delirious visions of me getting rich on translations of the poems. (I wish.)
This immediately complicated things because I was asking only for permission to translate (which is not just polite but required). I wouldn't dream of paying for the right to translate. As it is, I would be translating for free, though I am accustomed to being paid for commercial translations. In such case, the buyer of my services then owns what I was paid to do.
A translation of a literary work, however, is regarded as a new literary work in its own right. So I'll just move on to some other poet who is willing to allow me to translate their work and get some international exposure.