It is quite easy for people handy with a smartphone. https://www.gov.uk/apply-renew-passport. Make sure you take a photo against a plain white background. The bubbly paint effect on walls , popular in Spain
UK Passport Renewal at Round Town Travel Avda Dr Severo Ochoa 2, Benidorm
You can get your passport renewed here for about 160 euros or 30 euros if you are over 90. They send off your old passport and you will get a new one in the post together with your old passport in separate envelopes delivered by courier. Passport renewal con now only be done online or with smartphone so those not tech savy this is a good option.
Telephone 966 811123. If you do not live in Benidorm ask in a British owned business such as Estate agent etc to see if they will do it for you.