Will my plagiarism penalty damage my chances of a career in law?

I got a plagiarism penalty in my second year at university and I now realise I have to declare this to the SRA to get onto my LPC. I am scared it is going to damage my chances of securing a training contract.

In my second year of my undergraduate law degree I was given a plagiarism penalty on one of my essays. After this year I will have to declare it to the SRA as I want to do the LPC and I am scared it will count against me. The plagiarism was done completely by mistake – I know it sounds silly but after I read so many texts my words seem to get muddled with professional law texts – I didn’t deny it at the hearing after seeing the marked text but obviously tried to explain the error. Is having this on my record going to damage my chances of securing a training contract? Is there anything I can do to help my situation?