Mix flour, baking soda and baking powder together and mix well. Remove the leaves from the thyme until you have approx 3 tbsp full and chop them a bit. It looks like a lot but the flavor is quite subtle.
Put the butter into a mixing bowl and mix it till light an creamy. Add sugar and mix well. Add the eggs one by one and turn the speed of the mixer down after the last egg.
Now add 1/3 of yr flourmixture and 1/3 of the buttermilk, and repeat until finished. Add the juice of 1 lemon at the end of this. Spoon the thyme leaves through it.
Grease your bundt cake well. I tend to use melted butter and sprinkle the tin with flour. Tap the excess flour out of the tin and than ad the batter. Smooth the top and put into the oven for around 1 hr and 15 minutes but check after an hour if the inside is cooked. I've used a smaller bundt tin so I needed only 30-35 minutes. Again..checking is important.
Take out of the oven and leave to cool for at least 5 minutes (15 is better) before taking it out. Leave to cool completely before adding the icing.
Make the icing by putting the icing sugar into a bowl and add some lemonjuice until it has the desired consistency.