Which Jewish secondary are you looking at? They are all quite different in character.
All the schools expect you to complete a SIF (supplementary information form) which gives you "points" based on your level of Jewish activity. You can gain these "points" by doing things such as attending synagogue frequently, sending your child to a Jewish primary school or Cheder, or Jewish community action e.g. volunteering. In order to get enough "points" you would want to start preparing now e.g. start attending shul more often.
Currently about ? of Jewish children attend a Jewish school. The most popular reason why parents send their children to Jewish schools is the outstanding academic achievement. All the mainstream Jewish secondary schools achieve exam results far higher than their local non-denominational counterparts, and several are among the top comprehensives in the country.
Other advantages of attending a Jewish school are learning Hebrew (useful for going to Israel), kosher food, festival and Shabbat observance (probably less relevant to you as you are not very observant) and an active Jewish social life.
Disadvantages of attending a Jewish school are losing the opportunity to mix with individuals of all religions (and none) and backgrounds. I have heard that some Jewish schools have had issues with racism because of this isolation. I have also heard that some schools can be a bit homophobic. Although the education at all the Jewish secondaries is excellent, some areas of the curriculum that they sometimes fall down on (compared to non-Jewish schools) are languages (other than Hebrew), religious studies (other than Judaism) and music.
Advantages of attending a non-Jewish school are being able to mix with children of all faiths and backgrounds. They may be able to experience a wider more varied curriculum as time will not be spent on Jewish education. Many larger schools with larger Jewish communities may have a Jewish society, and this may allow your child to mix with other Jewish children within school.
Disadvantages of attending a non-Jewish school would be that as potentially one of the only Jewish children in their school, your child could feel isolated, and could encounter antisemitism. Conversely they may also be seen positively as the "token Jew" but in this respect may be expected to have a full knowledge and understanding of all things Jewish, which would be fine for a confident knowledgable child, but intimidating for a shy or less knowledgable child.
The most important thing would be which school, Jewish or non-Jewish, would fit your child best. Which school will allow your child to develop their own individual talents, whilst supporting them pastorally and giving them additional support in any areas they are weaker in?