I suppose that we have never considered the flat as a commercial endeavour
I think it is time that you did consider this flat as a commercial endeavour, since now is the time for doing the maths.
Very generously, your parents gave you two sisters deposit money to invest in a flat. Would either of you been able to afford a 100% mortgage? Probably not.
If you’d rented it out, you would each have taken 50% of the rent as joint landlords, minus whatever repairs and maintenance costs any property would incur. You would have set the rent to cover these extra costs and a bit more to pay off the mortgage, with any luck.
Have you calculated what a fair market rent would have been for your flat OP?
Instead of renting it out on a 50/50 basis, you decided to live there. You paid the mortgage. The mortgage was calculated on a sum that was £50k less than it would have been, so your monthly payment was considerably reduced and much more affordable for you.
Meanwhile your sister was paying rent to another landlord, who presumably was also covering their maintenance costs and a bit extra for profit/paying back a mortgage, whilst watching their property increase in value.
(Ignore the fact that your sister lived rent-free at your parents for a while, as it is not relevant to this. What they arranged between themselves is their own business).
So, by living in the property, you have accrued benefits that your sister has not. You have had security and you have paid a monthly mortgage which is a significantly better deal than any rent you would have paid to a landlord (ie mortgage on reduced sum (capital sum-£50k), no landlord profit). But you have also taken on the maintenance and improvements.
If you had been joint landlord with your sister all this time, you would both have had a rental income and your mortgage would have been paid off to the same extent, with any luck. When the time came to sell, it would have been an very easy calculation to go 50/50, as per your original agreement.
So, all this time your sister could have been receiving rent on the property you are living in. You haven’t been paying your sister rent but instead you have been paying the mortgage company. If you’d been renting that flat, you would have been paying a lot more than that monthly mortgage payment you are currently paying, for all of the above reasons.
In summary, you’ve had it easy. It’s nice that you kept the property well-maintained, but you would have been paying for that as the property-owner anyway. I would see that as the price you pay for being the one who got to live in the property, while your sister was being charged that premium in whatever rent she was paying.
I think you know that you are not being fair to your sister. Your tone in your post ‘I suppose’ this and ‘I suppose’ that, suggests to me that you are trying to wriggle out of doing the right thing here. Bringing up the fact that she lived with your parents rent-free smacks of childish whataboutery.
You don’t say how much you have ‘overpaid’ on the mortgage...did you chuck a lump sum in to pay a bit of it off with the aim of reducing monthly repayments? If you were savvy enough to do that, you were surely savvy enough to understand that it would have had an impact on your property ownership arrangements with your sister!
As far as I can see, the only extra cash you can retrieve from the sale of your flat would be if you had made a significant spend - say 10k on a new kitchen - that had massively boosted the re-sale value of the flat. Even so, you would have enjoyed the use of that kitchen so I wouldn’t expect you to re-coup the full amount. That’s your only wriggle room and you may decide to be gracious about it for the sake of family unity.
Other than that, keep to your original agreement.