Don`t forget January is winter in Tenerife just the same as the UK. Jan/Feb are the worst two months.
After saying that it will still be in the seventies during the day, evenings for sitting out possibly a pullover.
You always take the chance if you are only there for a week that some days could be cloudy but the temperature will still be the same.
Very little rain.
Much superior to Spain where the temperature drops and it can rain for England.
South of the island is dry and arid the north is lush and greener but with cooler temperatures and more rain.
Anything from Los Cristianos to Los Gigantes in the south is your best bet.
You could be lucky and get wall to wall sun for a week.
Someone else will be more knowledgeable on the other islands.
The thing is where do you go if not the canaries, options are Florida, Egypt or Goa unless you are going long haul.
Rodz

I am sure I read somewhere the warmest place in the Canaries in winter is the south of Gran Canaria.
I have been to Tenerife and Gran Canaria in January and Gran Canaria was warmer and sunnier.
You can check the weather for all islands on wunderweather.It also gives temperatures for the previous years.

Yes, the south of Gran Canaria is slightly better than the south of Tenerife for weather. In fact, it is the best climate in the Canaries for hot, dry & sunny weather. This applies to the Mogan region, which includes Puerto Rico and Puerto Mogan. Playa del Ingles and Maspalomas will be a little cooler than this region.

We own timeshare between Puerto Rico & Amadores and the weather is definitely a shade warmer and sunnier then PDLA & Los Cristianos but it's not that great a difference. We've had holidays in the south of Tenerife in January before we moved over here that were wall to wall sunshine, better than some we've had in September in fact.

thanks for the replies it will probably be gran canaria for us then . thanks again.