It is difficult to provide a definitive method for preparing for the ELAT, as the aim of the paper is to use unseen texts that are not covered by the school curriculum. There is not a set reading list that one should read. However, I do think it is extremely useful to get a feel for the layout of the exam. Reading short passages of prose from a variety of genres and periods will build your confidence in dealing with unfamiliar textst. When reading the passages, it may be worth analysing them, noting themes, symbols, motifs, specific language choices, and more broader concepts which stem from these. For example if you are discussing madness in an asylum, you might question whether the true mad men are those outside of it, unable to recognise their own insanity. I would also recommend reading some poetry and drama, and practise making links between different texts as this is what you will need to do in the exam. Wha themes do they share? How are they different? How are they similar? Is one more effective than the other in achieving its purpose?
Oxford offers practice papers and examiner feedback which will also be worth looking at. You can find this on http://www.admissionstestingservices.org/for-test-takers/elat/preparing-for-elat/