If you each give away your 1/3rd shares of the property, they will be both gifts for Inheritance Tax purposes and disposals for Capital Gains Tax purposes.
The gifts will be valued at the time they are made and will stay in each of your respective estates for seven years from the time they are made. Take a look here for information on Inheritance Tax.
The cost of the property for CGT purposes will be its probate value, ie the value when your grandmother passed away. So, if the probate value was about £80,000 and you sell it for £300,000, you will each make a paper gain of £73,333 if you give it away. Assuming, none of you have lived in the property during your ownership of it, the only relief you will each be entitled to will be the annual CGT exemption or tax free allowance which currently stands at £11,100. You would each have a net taxable gain of £62,233. This can be reduced by deducting the costs of selling the property (legal fees, selling agent fees etc). There is no taper or inflation relief I'm afraid.
There are two rates of CGT on residential property, 18% and 28%. The rate or combination of rates that you will each pay will be dependent on your respective incomes in the tax year you dispose of the property. Take a look here for information on how to work out your CGT rate.
I hope this helps but let me know if you have any further questions.