It might be Lagavulin but the thing is no one here will be able to tell you for sure.
Another thread suggests Caol Ila:
http://www.whiskymag.com/forum/viewtopi ... esco+islay
I know a few guys who work in the bottling halls at Broxburn and they don't know but they do admit to bottling most of the supermarket malts. The supermarket malts appear to be a closely guarded secret and allow distillers to shift excess stock without harming the brand name (and apparently can sometimes be Caol Ila one year and then Bowmore the next).
If you want to try what is widely suspected to be cheap Lagavulin, try one of Ian Macleods own label Islays.
I like the Sainsburys Islay Pure Malt as I think (but will never know) that it has some Ardbeg in the vatting and I also like the Morrisons (single malt) one as I think it is Bowmore.
Whatever they are they're great value and I will be sure to try the Tesco Islay and let you know if I think it is Lagavulin, but we'll never know for sure.