Creating own independent Internet Server.

There are two options: Either you order a 10/100 MB/s internet line from your internet service provider directly to your datacenter (which might be quite expensive) or you lease some rackspace at a provider of your choice and put in your server hardware.
Cheaper options would be to lease a dedicated (physical or virtual) server at a provider of your choice. This would give you 100% admin rights on the machine while the provider is responsible for the hardware, network connection, power, cooling.

I'm not entirely sure what you want to do.  However, I do know that there isn't a "main internet provider".  Each internet ISP or hosting company contracts with many services to provide connections to other internet sites.

This page http://www.heraklesdata.com/offerings.php shows the connections that a small data center in Sacramento California has contracted with.  These are not 'free' connections, they have to pay for them.  Note that most are telephone companies or 'common carriers' that support data networks.  This page http://navigators.com/isp.html lists some of the major network providers.

The idea of a single 'internet backbone' pretty much died 15 years ago.  The internet consists of a web of interconnections between providers now.  It is unlikely that you can afford to connect to enough providers to make your service useful.

Basically, I'm tired of ISP's in the UK. First of all, their service is terrible. It doesn't work half of the time and the other half it's just slow as hell. Besides, upload speeds are maximum 100 kbps... I need about 1024 because I want to stream stuff...

So I just want an independent connection, I guess.