Normality and homegeneity

I have performed certain statistical tests (ANOVA, DMRT, t-test, etc.) assuming my data is normal as well as with homogeneous variance. Now my paper is almost accepted in a reputed journal, reviewer asked me,"Is your data normal and with homogeneous variance". On performing Shapiro-Wilk test I came to know that a part of my data (one out of four treatments) is not normal. Similarly, a part of my data does not have equal variance. What should be my reply to the reviewer? Do I have to analyse my data again?

P.S. I am not a statistician.
P.P.S. Getting published in this journal really means to me.

Thanks.