Proof of employment

Hello,

I asked my past employer for copies of my P60s since I've lost mine. I've worked for the company from November 2011 until September 2015. They only sent me the copies of 2014 and 2015 saying that they don't have the other ones anymore.
Do you think the letter from the company stating that I've worked for them from 2011 until 2015 and the contract (stating that i've started in Nov 2011) is enough? I also have wages slips for 2011 and some of 2013, none for 2012.

Thanks and kind regards,
Elena