Assuming you did not work in Canada before coming to the UK, you will not be able to claim any benefits that come within the definition of public funds (e.g. child benefit, child tax credit). You are not entitled to any relaxation in tax due to having a child. You cannot claim council tax benefit.
If your wife has been working she may be entitled to Statutory Maternity Pay or Maternity Allowance as these do not come within the definition of public funds.
Do not listen to any health visitor, midwife or other healthcare professional who insists that you apply for child benefit a child tax credit as 'HMRC will tell you whether you are eligible' - they get it wrong and as a result you would be breaching the conditions of your visa.
See
Public funds guidance