I've just come back from Hotel Anthelia in Costa Adeje and had a wonderful british nanny. Lisa Roberts came to our room and was super with our 4 yr old and 7 month baby. She was also available in the days too but we enjoyed our boys company too much and just had her every other night.
Not cheap, at 15 euros per hour it added up over the holiday but after taking our 4 yr old out for evening dinner and the event being stressful we decided that she was worth it and not worrying to rush back.
I know that other quality hotels offer babysitting service but it was over £20ph Abama/Bahia so Lisa came out cheaper and I liked having the consistancy. Lisa also recommended restaurants and places to go/avoid.
You can view her website www.tenerifechildcare.com