1st amendment does not allow you do say whatever you feel like. Explicitly the following is not protected

https://en.wikipedia.org/wiki/United_States_free_speech_exce...

But regardless, you've conveniently only quoted part of that law text. It's only about electronic communication https://www.legislation.gov.uk/ukpga/2003/21/section/127

and for context the relevant parts read:

With 1a saying

   A person is guilty of an offence if he sends by means of a public
   electronic communications network a message or other matter that is
   grossly offensive or of an indecent, obscene or menacing character

and 2a saying

   A person is guilty of an offence if, for the purpose of causing
   annoyance, inconvenience or needless anxiety to another, he sends by
   means of a public electronic communications network, a message that he
   knows to be false

In other words, you're not allowed to lie for the sole purpose of "causing annoyance, inconvenience or needless anxiety to another" and you're not allowed to send messages that are "grossly offensive or of an indecent, obscene or menacing character". 1a is not allowed under 1st amendment, and we can argue about how the latter is allowed by the 1st amendment, but some of it surely isn't as obscenity, incitement, and fighting words and offensive speech are explicitly not allowed.