UK tax question...is this correct?

First of all, HMRC do not deduct tax from your pay - this is your employer's reposnsibility. Your calcualtions of tax due this year are correct and in order to make this work out, you need to be on the correct tax code. You are on emergency code as your employer does not know about the carer's allowance. You now need to ring your tax office (employer will have the number) and ask them to issue a proper code to your employer taking into account the carer's allowance. They may ask you to put this in writing. Once the ulative code is issued, your employer will make your refund.