There are hundreds of companies that would do this for you, and their prices vary dramatically. Try the yellow pages or if you can, get hold of a copy of the Costa Blanca News, where many advertise.
Once you have a price that you are happy with you will have to decide if it is worth transporting these items, or would it be cheaper to simply buy new when you get here.
It will be important to label all your items properly, and those that are fragile or cannot be stacked should be labeled in English as well as Spanish. Keep a detailed list of your possessions. Ensure that the Company that you use has insurance, and read the terms and conditions.

A second alternative is to hire a Luton van and do it yourself. You can be more or less sure that your stuff will arrive in one piece.

Lastly, you could advertise that you have an amount of gear to bring over. You may get lucky and find somebody in a similar situation and be able to share the cost.

Personal I would say it is not worth the cost to drive down with a luton van full unless you can get a load for the return journey. It will cost you at least £400 in petrol and tools on the motorway for the return journey plus the cost of ferry tickets for you andy passenger and the van plus a possible over night stop as it is well over 1000 milles.

If the apartment is going to be for rent then don't use your furniture buy some cheap stuff when you get down there, also how much furniture if any comes with the apartment and if it is new can you purchase a furniture pack of the vendor.