Hello,

I am doing a flight from EGLL - WSSS and I have some step climbs but I have entered the step climb from FL320 to FL330 but on the waypoint after it still shows FL320.

You didn't specify how you entered the step climb and where you are with respect to the step, and what you are using to plan the steps.  The 777 will automatically compute where the step climb should occur, if you are using a flight planner it may not agree with the FMS but always go with the FMS.  To manually enter a step, enter 330S at the waypoint on the LEGS page where you want to step.  Be aware that any steps before the manually entered one will be removed when you do this.  See also the FCOM 11.21.33.