If you are a common wealth citizen, you should be able to apply to come into the United Kingdom if you can demonstrate that you are 17 years old or over and you are able or plan to work, and you can support yourself in the UK without recourse to public funds.
Furthermore, applicants must show that at least one of their grandparent was given birth to in the United Kingdom (including the Channel Islands and the Isle of Man) or prior to 31-03-1922 in the region now referred to as the Republic of Ireland; or on a British registered ship or airplane.
It is important to note that you will be able to lay claim to UK ancestry regardless of whether or not your relationship to the grandparent is in the legitimate line or not. You will not be able to lay claim to UK ancestry through a step-parent. However you will be able to lay claim to UK ancestry if your relationship with the relevant grandparent is by adoption. Note that you will need to show proof of legal adoption in your application.