Pico 1.3 + ESP8266 ESP01 0.25.0.0 problem

That's really strange - are you using an up to date firmware on the Pico? And you're 100% sure that's the code you used?

I just tried your exact code on a Pico with 0.25 here, And I get this line:

["AT+CIPSTART=0,\"TCP\",\"w ww.pur3.co.uk\",80\r\n"

Note the "w ww.pur3.co.uk" and not "http://www.pur3.co.uk" - so I'm not sure why yours would be different?

edit: I had to add a space in the www so the forum didn't change it :)