Dave,
Unfortunately, Telefonica are notoriously slow at providing new land-lines and ADSL, but you can always do what we have done - rely on 3G mobile phone technology.
Several providers, such as Movistar (the 'mobile' arm of Telefonica) and Orange, offer a USB Modem which plugs directly into a USB port of your PC or laptop. These modems are about the size of a small mobile phone; you insert the 3G SIM card provided, plug it into your computer, register with the appropriate ISP, and off you go (the service is usually activated the following day).
The downside of these devices is that they are on a 'contract' basis - I had to sign an 18 month contract with Movistar, and I believe other providers are much the same. Apart from an initial 3 months at half price, our charges are 30 € per month (plus IVA). It may be, with competition and alternative providers, that the current deals are better than this.
The price will also depend on the download limit you choose; ours is the basic 1Gig per month and has been adequate for us (Jenny can be surfing for as much as 3 or 4 hours per day in total, and we generally only reach about halfway to our limit.) However, if you download a lot of music or video files or streaming TV/Radio you might need a more expensive package with a higher limit. Some packages now also seem to be linked to mobile phone and TV provision, so it is a good idea to look around at what is available.
As you might expect from a mobile-phone based system, it is not quite as robust as a land-line. The speed is a bit variable, plus, in the summer months when there are lots of visitors using up the mobile bandwidth, connection might be a bit hit-and-miss during busy periods. Hence I wouldn't really recommend this system for streaming.
Overall though, we have been satisfied with the service so far.
I'm sure other readers will have similar experiences to tell you about, and no doubt there are other pitfalls and problems we don't know about or haven't encountered, someone will be bound to let you know.
Ken.