Hi Emily
Moving abroad is a big decision and some planning before you set off is a good idea. There are seven islands that make up the Canary Islands, but the larger ones will offer better chances of work opportunities. First of all which island would suit you both best. There is a local website that gives lots of detail about each of the islands as well as local businesses on the islands. thecanaryislander.com All the islands are different and you need to decide what is most important for you apart from finding work.
Unemployment on the Canary Islands is high, but tourism is very strong here as the weather remains the same throughout the year, so it is an all year destination. The airport is always busy - the third busiest in Spain - and the tourist centres on the islands are full of people trying to escape the cold winter or find the furthest south you can go in Europe. So tourist areas have bars and restaurants that often are looking for casual workers - but low pay and long hours.
If you plan to stay and work here then you need to apply for a residency certificate - it is known as a NIE number. This certificate and its number is important for nearly everything here. If you do not speak Spanish, you can ask a gestor to do this for you or accompany you. They are like a lawyer in some ways not qualified to the same level. Or a Spanish speaking friend can help you. It is not difficult to do.
Many people have found living abroad is cheaper than living in the UK, but wages are less too. VAT on the Canary Islands is only 5%, so petrol is cheaper here than Spain and the UK. Council tax is less and car tax if you buy a car is less. Alcohol and cigarettes with less tax are cheaper too and Spanish restaurants offer meal of the day - menu del dia - for about 7 euros for starter, main course and a beer.
Life is at a slower pace and not everyone likes this. Things do get done, but not as quickly as many ex-pats from the UK would prefer. However the weather is hotter and drier and that alone makes people feel better.
The most important thing is to make sure you can support yourselves financially, because without money many people find life very difficult here. If you have special interests or skills, then you may find you can get work here. Many people have set up their own businesses here for diving, surfing, painting, decorating etc., but don't rush to buy a bar unless you have plenty of experience in running a bar.
With low cost flights here and some cheap accommodation around, it is a good idea to take a short break on the island you are considering and ask around about work opportunities and apartment rentals. Lots of people have already done what you plan.
Good luck