I have been visiting the Costa de Almeria for many years now with my family, and Almeria airport is the most convenient, but is also accessible from Murcia and the larger Alicante airport, where there are more abundant flights from the UK.
The particular area I visit is a section of the coast between Peurto del Rey and Mojacar, including nearby Garrucha and Vera. Mojacar is the ideal holiday destination, with hotels from large package types on the beach front to smaller boutique hotels in the village itself. The Moorish village of Mojacar is a short distance from the beach on a hillside, with a charming ancient layout of narrow winding roads and wonderful shops and cafes tucked away. The beach front, Mojacar Playa, is a very active community, home brilliant bars and restaurants, and I certainly recommend 'Badgers', a lovely family restaurant owned by British expats.
In summary, Mojacar has everything for the British holiday maker; beutiful beach, English speaking restaurants, and a rich history and culture.