Proving Unemployment to a new job (UK)

So I'm about to start a new job. They've just recently asked for proof of my times being unemployed over the past few years. I don't know why they need this btw.

Wouldn't be too much of an issue except on my CV I omitted a 2.5 week job that ended badly (earlier this year). As this was an apprenticeship, I was paid less than minimum wage and therefore wouldn't have paid taxed (if this matters at all).

I don't know whether a document will show the gap as me working or whether it will just show a gap. I just don't know what to do. I don't want to lose this job.

Please help.

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