Over 11% of Iceland is permanently covered by glacier. The largest is Vatnajökull in the south-east which feeds Jökulsárlón ice lagoon and can be accessed by guided tour from various locations between Vik and Höfn. For those who do not want to pay upwards of £50 a person it is still possible to experience a glacier and even without a four-wheel drive car.
Sólheimajökull is a tongue of the much larger Mýrdalsjökull glacier and is one of the most accessible in Iceland. At the end of road 221, a spur from the ring-road between Skogarfoss and Vik, is a gravel car park and café. Stop here and take the marked trail for a 15 to 20 minute walk to the foot of the ice. The website for the café, and a number of other online sources, advise that the road is gravel as soon as you leave route 1, and that the 5km journey will take up to half an hour. This information is a little out of date, or perhaps deliberately inaccurate to the keep the crowds away. The road is tarmacked until the car park and though twisty and narrow in places, completely manageable in a two-wheel drive car.
It is not advisable to climb on to the ice without the correct equipment and knowledge. The glacier is constantly moving and its recession has been rapid in recent years. Fissures open up quickly and unexpectedly; a fall through the ice is likely to be fatal. That said, at Sólheimajökull you can get close enough to appreciate the sheer size and depth of what is only a minor tributary of a glacier and, if you are lucky, you might witness the ice carving and falling in to the expectant river below with an ominous creak and thunderous sigh.
Sólheimajökull is close to the 2010 eruption site of the infamous volcano Eyjafjallajökull and a layer of black ash has ingrained itself in to much of the ice. Whilst this means that the glacier is not the traditional sparkling white of the tourist brochures, it is an interesting photographic subject, with the dark crust in contrast to the light crystals of the inside, visible in places where the ice has cracked and broken. An unusual and exhilarating experience, and all for free.
For more things to do for free in Iceland, see here.