Asda claim, both on their website and on their in-store advertising, that their phones will work on any network. If you bought a phone from Asda and found that it didn't work on a particular network you'd have the legal right to a full refund as you'd been sold a product which was not 'fit for purpose'.
To 'cover your back' it might be best, before buying the phone, to ask at the Customer Service Desk whether you can use the phone on the 3 Network - or, if you buy online, email Asda to ask the same question. However I can see no reason why the phone I linked to wouldn't work with your SIM card.
Chris