Well done your GP for letting you try. Believe me, that's not typical. Many newly-diagnosed have been put onto medication when they were barely into diabetes territory.
In terms of timescale, for me at least, when I was diagnosed my DN told me I had to get my BG into single figures before my next appointment two weeks later. Changed my diet and managed it the day before I saw her. It took another 4 weeks before I was getting both fasting and post-prandial readings that were consistently in range.
Martin