Correct, the MCB only disconnects the live wire. Neutral stays in circuit and it's kind of a pain - I had left a lot of cable loops and when I would cut them to add a face plate, the snips were shorting earth and neutral. I learned this the hard way!
You're tripping the RCD because you're bridging neutral and CPC ("earth"). This gives the current flowing through the neutral conductor two paths to ground basically, and the RCD notices that the current flowing through the live and neutral conductors isn't the same.
Now, when I work on a circuit I switch off the MCB and I lift the neutral from the neutral bar in the consumer unit. It's that, or just turn off all the electric basically.