I have figured it out. I activated the twentytwelve theme instead of my child theme and that worked with mobile devices so I figured it must be a child theme issue.
I went through the files of my child theme: I left .css and .rtf as they were and images file as it was.
Renamed functions.php to -functions.php and footer to -footer.php and hey presto it worked.
I have looked up a lot of stuff on this and suggestions range from deactivating plug-ins to cache issues. I am not techy but thinking about it, all the problems I have had with the site (previously not able to log-in), have been caused by the functions.php file in my child theme: it appears you do not need this for the child theme to work. Leave the parent functions.php exactly as it is and get rid of functions.php altogether, even if its got no code in it seems to screw things up.
I would be happy if someone could explain why the functions.php in the child theme seems so troublesome!?