were there any reasons for increasing the age?
Yes, because it was increasing the rate of unemployment overall
Raising of school leaving age in England and Wales
 In recent years, government statistics showed that 11% of 16 to 18 year-olds were neither continuing their education after completion of their GCSEs, nor in full-time employment or an apprenticeship, thus increasing the overall unemployment rate, given that many are unable to find work.
what is the minimum school leaving age in the uk It is 19 years of age from the year 2017
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Raising of school leaving age in England and Wales [SEP] Introduction
This left a gap year of school leavers who, by law, had to complete an additional year of education from 1973 onwards. In recent years, government statistics showed that 11% of 16 to 18 year-olds were neither continuing their education after completion of their GCSEs, nor in full-time employment or an apprenticeship, thus increasing the overall unemployment rate, given that many are unable to find work. The UK Government hoped that by making education compulsory up to the age of seventeen years by 2013, eighteen years by 2015 and nineteen years by 2017. it could change this.