Sorry, no.
The Canary Islands are outside of the EU, so you'd be allowed to bring in just 200 cigarettes, duty free, if you were travelling back from Tenerife. However you're not entitled to any such allowance for postal imports.
If someone posts 200 cigarettes to you, here's how your bill would add up:
Excise Duty (Part 1): The first part of the excise duty is calculated as 22% of the (UK) retail price of the cigarettes. So, if they sell for �5 for 20, that's 22% of �50 = �11.
Excise Duty (Part 2): There's additional excise duty of �105.10 per 1000 cigarettes, so for 200 cigarettes you'll pay 0.2 x �105.10 = �21 (approx).
Import Duty: This is charged at 57.6% of the purchase price of the cigarettes. A bit of web searching suggest that cigarettes might cost �1.30 for 20 in Tenerife, so the import duty will be 57.6% of �13 = �7.50 (approx).
VAT: This is calculated as 17.5% of (cost + excise duty + import duty) = 0.175 x (�13 + �32 + �7.50) = �9 (approx)
Examination Fee: There's a flat fee of �8 for the customs examination.
So the postman will demand approx (�32 + �7.50 + �9 + �8 =) �56.50 before handing over your cigarettes. That's dearer than buying the cigarettes in the UK, without even taking into account what your relative had to pay for them in the first place!
Chris