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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.
If you gift your mother your half-share in the property she lives in and that share has increased in value by more than £11,100 since your father left it to you then I'm afraid that you will have some CGT to pay unless it has been your main home during the period that you have owned a 50% share. However, if your father passed away less than two years ago, you could execute a deed of variation to his will such that your share of the property goes directly to your mother instead of to you and no CGT would be due. Take a look here for more information on deeds of variation.
I hope this helps but let me know if you have any further questions.