Very annoying indeed yes. There are various things which you are doing that are not ideal here. Personally, I would have avoided floating the elements in the header altogether and probably had one div with the safety services logo and the four accreditation logos all in one image set as that div background. You could ten have just nested the navmenu inside one header div but I am not telling you that you are wrong, everyone has to find their own way with css as that is the nature of the beast and there are many many ways!
Anyway for simplicity's sake and to preserve your own design method, just alter the height in the below div to 134px and I think you'll find your gap will disappear.
height:135px; ------ change to 134px