What exactly is a tax rebate, when are they given, how do you apply or become elligiable?
As you can see, I know nothing about them but wondered if I may be entitled to any extra money. 
If the terminology in the UK is the same as that in Australia, then a tax rebate is an amount that reduces your final tax payable for a given tax year. Rebates are usually granted to offset certain expenses e.g. medical costs or expenses related to raising children. You’d need to check with the UK tax people to see whether you’re entitled to any rebates.
So basically the equation goes:
Assessable income - allowable tax deductions = Taxable income
Taxable income x Tax rate = Tax payable
Tax payable - Tax rebates = Final tax payable