As somebody who used to oppose the minimum wage and actually bothers to read economic studies I can tell you that the evidence for direct increases in unemployment is very weak and that a number of labour market factors outweigh it.
Where there may be limited evidence is in employment growth (the raw number of future jobs created) however since the UK creates 700,000+ jobs with population growth of 400,000 I don't consider current minimum wage increases to be anything other than good.
I emailed my MP about an 18 year old being paid less than a 25 year old for the same work, and his response was basically "so what,18 yr olds don't need as much money". So I asked him what was in place to offer discounts on energy, food, rent, council tax etc for 18 year olds who are forced to leave home. No reply.
It's manageable if you live outside of London and the South East.