If you can compete with the supermarkets, or near to for a feasible delivery cost then I think it would be a great idea.
May use a low cost number, or free number such as 0800 and even have an online checkout service.
A girl I know who lives in Lincoln uses a service exactly like that and its brilliant, its open till late and delivery does not take long at all. If I get time I'll try and get hold of her and PM you a link.
In terms of marketing it, a student and leaflet passing outside the student union, maybe an incentive such as discount on the first order, or an order over X value.
Also, remember the majority of students are only at university between September - June, and usually January, May and June time is exam season. It is probably worth remembering that a lot of universities have 3-4weeks off for Christmas, and 3-4weeks for Easter so maybe there will be six/seven months of good trade which you may have to make up for the weakness over the summer, or look to market at the locals.
I'm a student personally and I'd use a service that delivers to my house, if it was as competitively priced and chilled like in a supermarket or local convenience shop

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Hope this helps.