I didn't have lunch today and so I had a big afternoon tea instead. That's the way to say it.

2 things, Tanya- first -rather than big tea break, you are talking about time so a long tea break or an extended tea break is the best way to say it. (extended means longer than normal). second- when writing a sentence the tenses have to remain constant. You start in the present then switch to the past tense. To rewrite it : At 12 o'clock I don't have lunch, so at 4 o'clock I have an extended tea break, and i tell people at 4 o'clock in the afternoon, " I don't get any time at lunch so I get a long tea break instead".