Yes, you can—but you'll have to play by a different set of rules. When it comes to transferring to another EU member, Britain is now classified as a "third country," which makes the procedure a little more difficult than before. You will be permitted to stay if you were a legal resident of Spain before to January 1, 2021. If that's you, then you should find out if there are any accommodation facilities available at Los Cristianos.
Another option is to look for work in another part of Europe. There are many other countries in the European Union, and they all offer different benefits. For example, Germany has an excellent system of unemployment insurance that can help you out when things go wrong at work.
Of course, there are also countries outside of Europe that may be interested in hiring British workers. The United States is looking for skilled people, especially engineers. China wants doctors and nurses. All you need to do is put an ad on the internet and wait for some good jobs to come up.
The last thing to know is that you should not spend your entire life waiting for something to turn up. Have a look around at other options first because there may be better opportunities somewhere else. For example, if you see a job that fits perfectly with what you want to do but it's only available in Tenerife, then go for it!
Finally, remember that everything depends on how much money you have when you arrive.
To begin with, the legal concept of "residency" in Spain is straightforward. If you spend more than 182 days in Spain in a calendar year, you are considered a "resident" by the government. If you are not a citizen of Spain, your period of residence must be longer than three months to make you eligible for citizenship.
When you apply for a residence permit, the Spanish authorities will usually require proof of funds to cover your stay in Tenerife and any possibility of becoming financially dependent on them. In addition, they may also want to know about your occupation, salary, and specific requirements related to housing, employment, and integration into local society. Your employer should be able to help advise you on these issues.
Residence permits are usually issued by the regional government of Tenerife (or its department of migration). You must provide evidence of having valid identification papers - such as a passport or national identity card - as well as money to cover the cost of the procedure. If you are unable to pay, you can ask the consulate for a letter of recommendation.
The whole process can take up to two years from the date of application. In the meantime, you must fulfill some obligations towards Tenerife's social security system.
You must, of course, be allowed to live in Portugal in order to relocate there. This is only a formality for EU citizens. For individuals who are not citizens of the EU, you must apply for a residency permit, the process of which varies depending on your status. The good news is that most people will not need a visa to visit Portugal.
Relocating to Portugal is easy because almost everyone has the same citizenship as you do and so can move here and work without any problems. In fact, many expatriates choose Portugal as their new home because it is such a flexible society where you can speak several languages and have access to different cultures.
People usually move to bigger cities like Lisbon or Porto for the more established economy but there are also opportunities in smaller towns near the Spanish border or on the coast. If you look around on the Internet, you should find plenty of information about finding employment in Portugal. The key thing is to get in touch with local authorities and see what jobs are available. You could also try contacting small companies or NGOs (non-governmental organizations) and ask if they may need someone to fill a position soon. Sometimes these kinds of positions don't go to locals first because they are looking for special skills or experience that non-EU citizens can offer. In this case, you would have to apply for a working permit.