The final squad for the Autumn internationals to be announced on Oct. 26.
"A couple of weeks ago I got a letter saying I was in contention. Everyone got (a) letter, reminding us what to work on. Mine said not to eat too much - to lose some weight," Vunipola told British media.
"I tried to look after what I ate and my diet during the summer. Eddie keeps you on your toes. I'm fighting for my place in this squad. Joe Marler's a world-class player so to have him back in the squad is a bonus."
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England, unbeaten since Jones took charge after last year's World Cup, host South Africa, Fiji, Argentina and Australia in November and December.
(Reporting by Ian Rodricks in Bengaluru; editing by Amlan Chakraborty)
