Hi. My name is*****'m looking at your question now and will post my answer or ask for more information here in a short while.
Your mother may have to pay CGT. You need to compare what the property was sold for for with what the cost is for CGT purposes. The cost for CGT purposes is the sum of one-third of the value of the property when your mother first became a joint tenant, one-sixth of the value of the property when the first parent passed away and one-half of the value of the propetry when the second parent passed away. Deduct that and the costs of selling the property (legal fees, selling agent fees etc) from the disposal proceeds to arrive at the gain or loss. The first £11,100 of gains made in the curren tax year, 2016/17 are tax free. The exemption for 2015/16 was £11,000.
There are two rates of CGT for gains on residential property, 18% and 28%. The rate or combination of rates that your mother will pay will be dependent on the leve of her income in the tax year the property was disposed of.
There may also be an Inheritance Tax issue. As your parents continued to live in the property after you took part-ownership, that means the "gift" was a "gift with reservation of benefit", a GWR. You can read about GWRs here and here. The value of the part gfited will have remained in your grandparents esates for IHT purposes at the time of their passing.
I hope this helps but let me know if you have any further questions.