As this question gets asked seemingly regularly (although not frequently), I thought it worth posting up this review by RegHardware.
http://www.reghardware.com/2012/08/18/ten_phones_for_seniors/
It might be useful in the future and tbh it threw up a few brands i had never heard of before so it is worth a look if trying to source mobiles for elderly relatives!
well my father has bigger hands than both you and me TL, so he has one of these
http://www.amazon.co.uk/dp/B002JOVMDY/ref=asc_df_B002JOVMDY9285393?smid=A3P5ROKL5A1OLE&tag=googlecouk06-21&linkCode=asn&creative=22206&creativeASIN=B002JOVMDY (http://www.amazon.co.uk/dp/B002JOVMDY/ref=asc_df_B002JOVMDY9285393?smid=A3P5ROKL5A1OLE&tag=googlecouk06-21&linkCode=asn&creative=22206&creativeASIN=B002JOVMDY)
While not being the most technical minded of folk, he can text and use the other functions on it :P
or do a search for big button mobile phones, you`ll be surprised as to how many there are !
As with everything in life the constrains of what you need, and the price tag will change all the search results, hope you find something suitable