Assuming the total estate was £153,000 and there were no gifts made in the seven years before her death which would bring the value of the beyond £325,000 (up to £650,000 if she was a widow depending on her late husband's estate's value), there will be no Inheritance Tax to pay.
There will be no Capital Gains Tax to pay on the sale of the house unless it is sold by your mother for more than £11,000 plus expenses of sale (the annual CGT exemption) more than it was worth when your grandmother died.
If your mother sells the property and gives you 50%, she will have made a gift which will be a potentially exempt transfer for Inheritance Tax purposes. So long as she lives for at least seven years after making such a gift, it will not be included in her estate for Inheritance Tax purposes.
In order to avoid the potentially exempt transfer scenario dexcribed in the previous paragraph and its potential IHT tax implications for your mother's estate, all the parties affected could make a deed of variation to the will such that it is amended to leave you half the house as if it had been wilfully left to you by your grandmother. You can read about such an arrangement here
If the property becomes jointly owned by you and your mother, then it could be sold for up to £22,000 plus expenses of sale more than it was worth when your grandmother died.
I hope this helps but let me know if you have any further questions.