The message they display says:

  We're sorry but this site is not accessible from the UK as it is part of our
  international service and is not funded by the licence fee. It is run commercially
  by BBC Worldwide, a wholly-owned subsidiary of the BBC, the profits
  made from it go back to BBC programme-makers to help fund great
  new BBC programmes.

The rationale is explained in a little more detail in a BBC FAQ [1].

BBC Worldwide is a commercial entity, but the BBC's fair trading rules prevents them from promoting a commercial entity to UK licence payers. The somewhat odd outcome is that BBC content is unavailable to people in the UK.

[1] http://www.bbc.co.uk/faqs/online/website_changes

Some parts are entirely blocked.

Somehow it's OK if a random person in Afghanistan accesses it for free, but when a BRITISH person in BRITAIN tries to access BRITISH broadcasting corp content then the funding model somehow matters.

Its beyond retarded.

bbc.com is specifically for international audiences, whereas bbc.co.uk is for the UK audience.

bbc.com is blocked within the UK because it is funded differently.

"We're sorry but this site is not accessible from the UK as it is part of our international service and is not funded by the licence fee. It is run commercially by BBC Worldwide, a wholly-owned subsidiary of the BBC..."

IIRC, because they receive funding from taxes they're constrained on what they can post for UK consumption.

Some stuff isn't available in the UK. It's not even a paywall. It's pretty silly.