A good offer there!
If you have a conventional ADSL contract, it may include webspace (I've got two, and they both do). Tell us who provides your ADSL, and I'm sure someone on here will soon tell you if you have webspace and how to access it.
Otherwise, you need somewhere with FTP access to upload your pages - FileZilla is indeed the one to use. Aerouk's space will help for the initial setup. If you get serious about the website, you will eventually want your own domain and space.
Don't be suckered into paying big money for a domain and hosting. You can register a .uk domain for around £6 for two years, with web and mail forwarding. I've got 23 domains registered in that way (not all for me, but for organisations I look after). Most of those are hosted on the same block of webspace with the same provider.