The nearest airports are Region de Murcia International Airport - RMU
There are many low cost airlines that go to Murcia including Ryanair, Easyjet, Jet2, which fly from most UK and many European cities. Alicante airport is an extra hour up the coastline and offers many more flight options.
If travelling from Alicante you need to hire a car, but it can offer more morning flights if on a short trip can make it very worthwhile. Low cost airlines are great if you stay within their rules; read their small print. Murcia Flights are available from many different airports in the UK and through six different, UK based low cost airlines.
The flying times for all flights to Murcia Airport from the UK are around 2 hours and 30 minutes