I am working on an SVN repository and do not want to create a new SVN branch. Instead of that, I want to create a branch local to my machine, something which could be done easil
I'm afraid you will have to create a new branch and keep merging any changes into it. The only alternative is to simply checkout the branch, keep updating and don't commit (or keep switching prior to commits) until you are finished. You could always have two working copies if you need to work on the original branch/trunk. Nowhere near ideal, but that's the way SVN works, which is still very good given the alternatives at the time.
I personally manage local history if that is what you are after via my IDE (Eclipse).