Hi agarima
KT3 straddles both boroughs just to confuse! See here for more information.
However, being in one borough doesn't usually preclude you from applying (or possibly getting in) to a secondary school in another borough, particularly if you live on the borders twixt several (unless they've got specific postcode catchment rules such as some of the SW London grammars have) and meet the entrance criteria (e.g. regarding distance twixt home and school/sibling policies etc...).
Indeed in London it's often the case that your closest secondary school can be in a neighbouring borough rather than the one to which you pay Council Tax! For example, for children in the Tooting Borders/Figges Marsh area (and just into Merton), Graveney (a Wandsworth school) is the closest secondary (although it's so sought-after and has such a small catchment area that even some who live closer than the just-into Merton residents may not qualify on distance criteria!).
I'm sure there will be other Merton Mumsnetters who can cite cases of secondary school age children in Raynes Park/New Malden/West Barnes (and indeed further into Merton) who attend Kingston schools. Certainly, there are Merton children who attend the Tiffin Schools.
Worth checking your queries with the Education Departments at Kingston and Merton Councils - and the schools you're interested in, so that you are in full possession of the facts!
You could also ask Merton Mumsnetters about their experiences of local secondary schools.
Good luck!