Contract to sell a property

Hi My sister agreed to sell a property to me 2 years ago for 100k and asked to pay her mortgage payment(intererest only about 150 pounds)and maintain the property while i live in it until i can arrange 100k. I have been paying that amount and maintained the property to high standard thinking it will be my house. Now i have arranged finance and she refused to sell the property for 100k and rather asking for 200k. When we did agree it was documented as bullet points on paper and she emailed a copy to me . This document is not signed but it is from her email and i have proof of paying the agreed amount and maintenance of the property.. Since she refused to sell the property i stopped making any further monthly payments and emailed her the reason for it is because she is not selling the property to me. She said its not an agreement because she never signed it but i think me agreeing to terms by paying and maintaning is enough for it to be binding and i can claim this in the court. How strong is my case