hi Jamie ,
Sorry to hear of your loss , I hope you can find out all the advice you need , there was a thread recently about this.
http://www.holidaytruths.co.uk/forum/taking-human-ashes-onboard-t159994.html?hilit=Ashes
There are really three parts to this ,
1 . Security , 2. Airline and 3 . Location .
I can advise you that in regards to security , as in leaving the UK and passing through security to the flight , you can carry an urn containing ashes through security with no problem , this is a normal procedure and happens quite often , it's just respectful from all sides concerned if you mention that you are carrying ashes when you are presenting your bag to go through the x ray , it saves anyone feeling disrespectful or awkward or upset .
In regards to airline , as far as I know this is not a problem for arlines , but as there are quite a few different airlines you could choose to fly to Tenerife , it would be best to check their individual website and search for this information , I'm sure you will have no problem .
In regards to location , just make sure there are no restrictions on entering that country with ashes off hand I don't know about Tenerife , the link I added above was mentioning Tenerife , so perhaps Fiona might be up to date with info regarding that .
Hopefully you will find a special place , that might comfort you and your mum at this sad time .