Can I still claim my notice even though I have started another job?

Usually, you have to give credit in an unfair dismissal claim for income earned after your employment has ended.

If, however, your employer doesn’t pay your notice and your notice pay forms part of your unfair dismissal claim, you are still entitled to be compensated fully in respect of your notice period, even though you may have obtained alternative employment during that time. This principle is commonly referred to as the ‘Norton Tool principle’ and effectively means that you could receive double pay for this period.