>And although I really really looked I could not find any explanation of the name.

blue pe·ter (blû pç'tər)
n. Nautical.
A blue flag with a white square in the center, flown to signal that a ship is ready to sail (courtesy of Atomica)

The programme's logo is a ship in a bottle and the music is the hornpipe. It was the main BBC children's magazine programme for many years and has a very loyal following.

It was famous for the things it made, using "sticky back plastic" they never used the tradename "Sellotape" and old breakfast cereal packets

Here is a rather typical spoof:
http://www.ashtons.demon.co.uk/c1/blue/blue.html