I would say it's very unlikely that Tesco will offer conversion to VS miles along with BA miles - BA will almost certianly have a exclusive deal on this. It is rather annoying to read the BA forum on FlyerTalk and see how easy it is to earn vast quantities of miles at Tesco. It would seem it's a far easier method than actually flying BA

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Nectar, IMHO, would be the obvious choice since they do not offer miles conversion to any frequent flyer scheme at present. Unfortunately it seems Nectar is at death's door, with Barclaycard no longer offering Nectar collection to new customers and some sources suggesting Debenhams and Sainsbury's are considering their future involvement. See this article:
http://news.bbc.co.uk/1/hi/business/3353509.stm