Depending on how involved your Handicap Secretary is you should be able to submit scorecards (outside of competitions) to bring  your handicap down, but I'd recommend that you only submit cards that you know will reduce your handicap rather than submitting all of your cards for your Handicap Secretary to determine.  These scorecards should, however,  be signed by yourself and your playing partner who should hold a current handicap.  If the round is played away from  your home club then you will also need to have their Club Pro countersign to prove that the round was played there.

There is also a rule (19) where your handicap can be cut using the 'obversation' rule where it's 'determined' that your playing ability is better than your current handicap,  based on this, if  you feel your handicap should be lower then you can also request it to be cut.