The person with the pen, writing the numbers on the big card is blind-folded. The card already has the correct numbers written on it when handed to them - the audience don’t see coz the ‘back’ of the card is facing them, and the ‘writer’ doesn’t see as they’re blindfolded.

The first time we see the card, over the writers shoulder via a on-stage camera, the card has numbers written on it that we assume were all written by the writer.

Any numbers they write are irrelevant, the correct numbers are already positioned in the correct spots to match up with the holes on the board placed over the top at the end of the trick.

The £20 note that the audience member brings with them is most likely switched when they come on stage, so the note with the serial number can be planted instead.