You're seriously misunderstanding how broadband, hosting and websites work.
Let's say you get 8Mb broadband. (20M broadband or cable isn't much better than this example)
In the UK on a home class line you get at best 8Mb Download 448k Upload.
Upload is the speed YOU send data to the internet. In other words it is the maximum possible speed your website visitors (ignoring more than one at once) can download a file from your site. You'll be pleased to know upload is almost never included in the data transfer limits by broadband providers.
You can run your own server over broadband, but this is typically for light traffic or hobby sites. You'll be limited to normal broadband speeds and contend with the fact it is a shared service - your users will be sharing that 448k upload speed with other users of your website, and any other traffic on your broadband block. I have no idea what broadband contention ratio is these days.
The other way of hosting at your own premises is via a leased line. They are ridiculously expensive, so we'll completely ignore those.
You could go SDSL or VDSL which give faster upload speeds - Upload 2M to 10M at best and £300+ per month.
Look at http://www.zen.co.uk or http://www.spitfire.co.uk for SDSL/VDSL providers. Both are business grade providers with good reputations.
So, the only affordable option left is web hosting at a data centre...
- You can have a "colocated" server at
a web hosts' data centre - You
own/rent the server at their
premises. They may handle backups.
They will have tools for you to manage it remotely.
They have a chunk of backup power,
fire extinguishers and the like.
- You can have a "VM" server at a web
hosts' data centre - Same as above,
but cheaper, as you only get a
part of a server.
- You can have a webhosting package -
You get some shared space on their
server, but won't decide what it runs
outside their defined limits (for instance you won't be choosing your own Apache modules). They
will almost certainly exclude file
downloading hosts in their Ts & Cs
With colocation you almost NEVER get the opportunity to buy your own hardware and send it to them - you choose one of their own offered servers - from their point of view it's the only sane option. It makes replacement and repair feasible if they are all the same make. From an admin point of view, all being on the same OS means they can offer backups and the like.
A VM server is probably your easiest and most cost effective option. I'd look at http://www.memset.com/ as Jeremy suggested.