Kollies Genealogy

According to the stories I’ve been told throughout my life, I am a direct descendant of JMW Turner (he’s supposedly my GGGGG Grandfather).  However, the children he had that would make me be related to him were illegitimate, and never took his surname.

Are there any JMW Turner experts out there who may be able to help?  If there is please get in touch, I want to prove/disprove this theory once and for all.

Here is my family line up to where I believe JMW Turner would join:

Me - My mother - My Grandma - Annie Pover - Eleanor Cooke - Emma Turner - William Turner - JMW Turner

Please prove or disprove my theory, I have very little evidence except stories passed down through the generations