Whilst there are distinct advantages to renting through an Agency, you need to be prepared for the fact that they are in business as a middle man to make profit, and as such you may find that you get a much better deal by looking for a private landlord.
There are many of them about in these areas that are either English, or speak a good standard of English, and as long as you insist on a fully legal contract, written in both English and Spanish and veryfied by a Lawyer on your behalf you should be fine.
Javea in particular is in quite a lot of demand for this kind of rental, and you may find that your money goes much further if you are prepared to look just a few miles further afield to places like Gata, Jesus Pobre, La Sella , La Xara, Benitachell etc... still only about 15 mins from The Coast but with a slightly more Spanish feel to it, and where a 750 Euros per month budget will go much, much further.
Here are just a few things that you need to consider whenrenting a property in Spain