Just one thing I'd add Chewy, before you nip off the dead buds, check that they are not actually chillis forming.
Hard to tell from the photo, but that is how the flowers look when a chilli is starting to form. the actual petals brown/die off, and a chilli begins to form underneath.
Oh and if you've got a good spot indoors and out, and it is not too much trouble, why not move it in and out, depending on the weather
Martin.