The Astronomical New Moon is on Wednesday 13 January 2021 at 5am. The crescent is not visible on this day.
The calculations for crescent visibility on Thursday 14 January 2021 for London is as follows
Moonset 5.41 pm
Crescent age 35 hours 29 minutes
Moon lag time 1 hour 11 minutes
Crescent elongation 18 degrees 41 minutes
Crescent altitude 8.03 degrees
Crescent can be easily seen on this day.
1st Jamadil Aakher 1442AH will InshaAllah be on Friday 15 January 2021 in Europe