Is it possible to have TRULY unlimited internet?

[Miss Shy]

I am quite a big Skype user as that is the only way for me to contact my family. I share my internet connection with 2 other people at home. They mostly use the Internet for youtube and facebook. We don't really download anything other than what needs to be downloaded for these 3 to work. We're using BT Infinity which is supposed to be unlimited but somehow we managed to go over the fair usage limit. My questions are: Is Skype really bad for download (if anyone knows how much it uses an hour that would help)? Is it possible to sign a contract for Internet that says unlimited and IS totally unlimited?
Also I thought of a way to go around this and using the Internet on my phone sounds like a plan. I'd pay for it and all but do I still need line rental? We use a BT landline and don't need another one but if I wanted to use BT WiFi independently (to lower the download) it looks a bit pricey. Can I use say EE internet having an EE mobile phone?
This is dead confusing... please help

[Dear Geek]

Well the approximate Skype usage details are:

~40MB per hour (Voice Chat only)
~120 MB per hour (Video Chat)

When you watch videos on YouTube it is same like downloading video. So watching videos consume most of your internet data.

[699]

Yes. I have always had completely unlimited internet.
I have AT&T U-verse high speed internet. and there is no usage limit. Before I got U-verse I had AT&T DSL. It also was unlimited.

[Boss]

Yea there great deals on the broadband market.

[george]

It is depend on your broadband how much you have bought internet limitation.