You can work, it just automatically stops your maternity leave but as you’re in the unpaid bit anyway it wouldn’t really make much difference. However you’d need to find out if you are allowed to work for this other company whilst still technically employed by your former company.
Thank you both. I'll look into these options x
You might also need to read your employment contract if you need to pay back the extra maternity pay from your employer (above SMP)
As soon as you take on paid employment, your maternity leave will finish even if it’s unpaid. You can ask your current employer to allow you to not service your notice period seeing as you wouldn’t be working during it anyway, and take on the new employment.