no, you can't send anonymous messages on any UK network to my knowledge, you certainly an't on Orange. The message will be rejected by the SMSC if it doesn't find a valid number/company shortcode on it. You coul dpossibly send from one of the services online that let you send free texts but most of those seem to require a valid phone number. You could always get one of the free SIMs that the networks give away regularly if you need a disposable number.
I should probably add if you're intending to do something to harass someone, bear in mind this is a criminal offence and the mobile networks can, in theory, pass your details onto the police if you're found to be engaging in such an activity. Not saying you will do but anybody else reading this thread could do if they were that way inclined.