The problem with saying sister should get 25% of the current value, less the costs of any improvements the OP has made is as follows.
Firstly, the fact that OP has spent eg £10,000 on the house does not mean the value of the house has therefore increased by £10,000. That is very often not the case, and she has chosen to spend that money and has enjoyed the benefits she perceives thereof. (In a very worst case scenario, sometimes so-called improvements can actually damage the market value of a house - not that we have any indication that is the case here, but it can happen, as we all know).
Furthermore, OP has made these improvements off her own bat, and in the full and certain knowledge that she was renting and would one day be moving on. I doubt her sister was consulted much, despite the fact she is an owner every bit as much as the OP. How often do we see people who are renting advised not to overspend their own money on their home?
She expects the sister to effectively pay 50% of these works she has had the benefit of - but her sister only owns 25% of the property and will only receive 25% of any uplift in value achieved on the sale. By her own logic, OP should be expecting the HA or whoever owns the majority 50% to pay half the cost - but of course she does not, as she knows that is not how it works.
Exactly the same logic applies to her sister.
OP you have benefitted massively through your sister's agreement to defer the sale, paying only 75% rent for all that time. You were completely unreasonable to get her to agree she would only get 25% of the probate value, regardless of when the future sale took place, possibly preying on her naivety. I struggle to believe any court would uphold that.
By living in the property, you seem to acquired some notions that you have some moral and legal rights with regard to it. You are wrong, your sister owns it every bit as much as you do, and has already suffered by tying up her capital to help meet your housing needs.
Do the right thing by your sister, and avoid a totally unnecessary rift in family relations in the process.