Need some advice

I signed a statement of fact saying I was unemployed during this period which is true but I took a job which lasted for 6 months and then went back on jsa but was volunteering one day a week which is clearly shown on my CV that it was volunteering. but I did not include the recent period on my statement of fact. Should I tell the company that I missed a period out on the statement of fact?

This is a matter between you and the company - we cannot know what facts they expected you to disclose.