My solution to parse a list of list of strings.
package stackoverflow.answers;
import java.lang.reflect.Type;
import java.util.List;
import com.google.gson.Gson;
import com.google.gson.reflect.TypeToken;
public class GsonTest {
  public static void main(String[] arg) {
    Gson gson = new Gson();
    String jsonOutput = "[[\"-1.816513\",\"52.5487566\"],[\"-1.8164913\",\"52.548824\"]]";
    Type listType = new TypeToken<List<List<String>>>() {}.getType();
    List<List<String>> strings = (List<List<String>>) gson.fromJson(jsonOutput, listType);
    for(List<String> inner: strings){
      for(String s: inner){
        System.out.println(s);
      }
    }
  }
}
But since values can be "thinked" also a doubles, you can parse them directly changing type into solution:
package stackoverflow.answers;
import java.lang.reflect.Type;
import java.util.List;
import com.google.gson.Gson;
import com.google.gson.reflect.TypeToken;
public class GsonTest {
  public static void main(String[] arg) {
    Gson gson = new Gson();
    String jsonOutput = "[[\"-1.816513\",\"52.5487566\"],[\"-1.8164913\",\"52.548824\"]]";
    Type listType = new TypeToken<List<List<Double>>>() {}.getType();
    List<List<Double>> numbers = (List<List<Double>>) gson.fromJson(jsonOutput, listType);
    for(List<Double> inner: numbers){
      for(Double d: inner){
        System.out.println(d);
      }
    }
  }
}
Not important in the context, but for future references: Java 7, Gson 2.2.4