The "Rights" bestowed upon current shareholders have a value. This is because the new shares to be issued are usually offered at a discount compared to the current market price. The value of the Rights is usually a little less than the difference between the current market value and the Rights Issue price. People buy the rights which then entitle them to buy the discounted shares.
What has happened with Bradford & Bingley (and indeed to HBOS and Barclays, who also recently launched Rights issues) is that the market value of the ordinary shares has plunged since the Rights issue price was announced. Investors can therefore buy shares for less on the open market than they can under the Rights issue.
This makes the Rights worthless and indeed also means that the Rights issue will fail to raise any cash from ordinary investors. To protect themselves against this the Rights Issue is "underwritten" by investement banks and they guarantee to take the shares at the Rights Issue price if this happens.
For ordinary investors these recent Rights issues are effectively dead in the water