There is a 'National Living Wage' and also 'London Living Wage', while the benefit system is uniform. People living in London who are affected by poverty especially during these times have the same benefit applied as someone living up north.
This doesn’t account for the different costs of living across the UK. I believe for people on benefits, their mental health and wellbeing is partially affected depending on how much they receive. Furthermore every region has a different cost of living, from the cost of a haircut to the cost of a house. However UC is paid the same no matter how high or low the local cost of living is.