Having been flying in and out of south-west Spain several times a year for almost a decade, I would agree with your correspondent Robin Springett (Bird Watching Nov 2016) that Malaga airport is often overcrowded with long queues for various services (although it does serve a lot more regional airports in the UK than any of the alternatives). However, I am surprised by his comments regarding Jerez airport and his recommendation of Gibraltar.
Aeropuerto de Jerez has a good range of hire car companies, four or five of which have booths allowing you to sort out your rental while you wait for your luggage (Sixt and Hertz are offsite but well served by a courtesy bus).
Far from having poor access, the airport has excellent links to Spain's motorway network. While it takes twice the time to drive to Tarifa from Jerez airport than from Gibraltar (90 mins vs 45 mins), the potential for delays at the Spain/Gibraltar border can often negate this advantage.
In addition, there are a number of superb birding sites (e.g. Mesas de Asta marsh, Langunas de Puerto de Santa Maria, Laguna de Medina and the Bonanza area) within 15 to 35 minutes of Aeropuerto de Jerez making flying there no chore.
In contrast, according to their website, Gibraltar airport is only served by two hire car companies, although there are more just across the border in La Linea (to which you have to walk). Flying into Gibraltar, though, has a very significant Achilles heel – frequent high winds and hence a tricky approach.
It is even sometimes listed as one of the world's top 10 scariest airports to fly into which, although rather 'over the top', indicates why nervous fliers might want to avoid it.
However, the real drawback is that when conditions are difficult flights are regularly diverted to Malaga so not only do you have to negotiate those queues after all but several additional hours and much inconvenience are added to your journey.
Hence, if Stansted (from which flights to Jerez depart) is not too inconvenient, I'd recommend flying into Aeropuerto de Jerez.
Indeed, I'd even prefer Seville airport over Gibraltar. Seville is, admittedly, much further if you plan to be based in Tarifa (c2 hrs) but the road network is excellent so the journey is not difficult.
It also has the distinct advantage that it allows you some interesting detours. If you're heading due south, depending on the season, you can check Brazo del Este (good for wetland birds inc. Marbled Teal and various introduced species), various sites for the elusive Rufous Bush Chat or the newly restored Laguna de los Tollos for White-headed Duck.
Alternatively, a longer detour to the east along good a motorway gives you a chance of exploring the Osuna area for species which are hard or impossible to see further south (e.g. Great Bustard, Black-bellied Sandgrouse & Roller).