WTF?
Why do you care that non-Christians, who live in a country that shuts down at the end of the year because of a Christian holiday, wish each other non-Christian greetings? Or, indeed, why decent Christians might wish non-Christians non-Christian greetings? You're not the only person living in the UK. People are allowed to talk to people other than you and your Christian brethren.
And is Christmas not a holiday? So, can you not stretch your imagination as far as "holiday includes Christmas"? How old are you? Season's Greetings cards have been around in the UK for decades. We've ALWAYS sent those out, never Merry Christmas cards.
Have to say, the irony of a Christian taking offence at being wished a happy holiday is quite something. In reality, what you really want to say is "every other religion and every atheist and agnostic person should bugger off and respect ME in my BRITISH, CHRISTIAN country because you don't count as much as I do as a superior Christian British person" 💁