One of Benidorm’s strengths is it’s excellent transport and communication links.
The most popular airport is Alicante-Elche at about 45 minutes away although Valencia is another option only 90 minutes away. San Javier-Murcia is a final choice although you would need a car to get to Benidorm easily. There are direct buses from the airport to Benidorm. There are also car hire services.
The nearest train station is Alicante with high-speed (AVE) links to Madrid. The RENFE site is (almost!) in English.
A tram runs along the coast from Alicante city to Dénia (with a scheduled change at Benidorm). The journeys are prompt and the trams are clean and spacious. The website is also in English.
Benidorm has an excellent bus station about two miles outside town, next to the motorway tolls. There are regular connections to the local towns and villages as well as many long-distance connections throughout Spain. There are regular departures for Barcelona and Madrid and even more regular departures to Alicante and Valencia. The main company is www.Alsa.es but cities like Teruel and Zaragoza are served by Grupo Autobuses Jiménez.
Eurolines run regular international services into Northern Europe although if I were to contemplate the long haul to London, I’d take Alsa to Barcelona. From there, Megabus run twice daily luxury coaches to London Victoria.
There is an excellent local bus service run by Llorente (Avanza) with inexpensive, regular journeys throughout Benidorm and its immediate area. La Nucia is however served by Alsa.