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People should never try to explore and look for ice caves on their own ! You should always hire a local guide that knows the ica, and it´s nature, since many ice caves are extremely dangerous, and ever changing. People have been crushed to death, when ice caves collapse without an obvious warning.
But this local expert (probably the most experienced glacier guide in Iceland) has knowledge in this field, why not contact him? http://www.localguide.is/localguide/Ice_Cave_Tour.html

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The ice cave you saw in those photos almost certainly no longer exists, as it was located where a glacier calves into a lagoon, and thus it would have collapsed in teh summer following when those photos were taken. Svinafellsjokull is an active glacier, melting into a lagoon, and thus changing all the time..

Ice caves form from time to time at the melting front of the Svinafellsjokull glacier (at Skaftafell), but are only briefly stabilised and accessible when the Svinafell glacial lagoon is frozen in midwinter sufficiently for you to walk on it to get to the summer ice/lagoon melting location,. So seeing such caves is a winter touring possibility only, and cannot be guaranteed even then as it is different every year. Here is one tour that offers the possibility of walking on the frozen lagoon to look for caves, suggesting it is an easy walk. But for reasons that should by now be clear, they can offer only the possiblity of finding such caves, not the certainty of seeing any particular spectacular cave. http://www.extremeiceland.is/winter-tours/iceland-break

The most reliable ice caves in Iceland are at Kverkfjoll, a location deep in the interior on the northern edge of the Vatnajokull ice cap. The caves form because the glacier edge lies over hot springs which melt the ice and keep the cave persistent. You can go on day-tours and multi-day tours to Kverkfjoll, operating out of Myvatn, from about late June to late August. The caves are about 3km from the road. The multiday tour will take you on a longer walk to see further wonders. No doubt if you hired a robust jeep you could drive there yourself, but a guided tour would offer the best chance of actually finding what there is to see there. The roads to get there can be expected to be open from about mid- or late-June maybe into September, but sometimes they close in late August. Google it for pictures and tour info.

There used to be a persistent cave that was regularly visited at Hrafntinnusker, accessible in summer only. But ice caves are dangerous places, especially in summer when the ice is melting, and a few people were killed there and eventually the cave collapsed entirely.

Many tourists today in Iceland go on the regular guided glacier walks (guide essential unless you are an experienced and equipped mountaineer) onto Solheimajokull, near Vik. There can be caves there. But what you see varies all the time, as the glacier is very active.

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thanks guys these are very helpful, i'll check out the links and see if they can offer a tailored tour