In reply to adamholden:
I did it at the end of July last year. It's a great route and well waymarked so you'll rarely need to consult the map.
B1 boots aren't necessarily. We both wore lightweight fabric boots. Saw some people wearing trainers!
We had a small bit of ice on the first day near the first hut but it was easy to skirt around. You could have a bit more in June.
If I were to do the route again, I'd opt for trail shoes with scree gaiters. Can be dusty crossing the volcanic sand.
Be prepared to cross rivers. I carried crocs on my pack. Poles are handy as they help to keep balanced.
We camped at the huts. The first hut on the glacier has no showers but the rest do. The Icelandic hiking website is spot on for information.
We booked coaches from Reykjavic with Reykjavic excursions. We opted for the hiking passport which offered multiple pick ups on the route. It's a fixed price regardless of how and when you book.
Feel free to message me if you want more info.