You can fly from Tenerife to Jerez or Seville directly but the drive down to La Linea is futher than from Malaga airport. But you can see the green scenery and stop off for tapas....and then fish and chips in Gibraltar!!
Great shopping in Gibraltar all the UK shops and so near to Spain. I bought all my Christmas food in Morrisons and it was a lot cheaper than buying it from Iceland the mark up in Iceland at Las Chafiras and Los Cristianos is remarkable

But really there isnīt much option if you want to buy British produce in Tenerife.
I would say that when you go to Gibraltar it is easier to walk over the border than to go over by car, and then you can get around the shopping streets on foot, the buses are very frequent and go right around the rock.
Another thing to remember is to take your British passport if you try to use your Canarian Residencia they wonīt let you in, as strictly it seems that it isnīt proof of your nationality and identity and neither is the scruffy new piece of paper they issue in the Canaries. You need your passport!!