but advised to pay her if I can afford it, remove her from the mortgage (which is a fraction of re-mortgaging) and if I can afford to stay there, carry on and take over the payments.
Sounds like good advice.
If house is valued at same as when you bought (and you both agree on this point) it that gives an easier starting point.
Do the maths of how much you have each paid in, including any decorating/work/upgrades (as you will benefit from these if you keep). Be fair, make sure its clear what is what (fully itemised, full amount and % paid.. In excel it would be 4 columns, Item, Full Cost , A share, B share).
At bottom to a total amount then also % split them.. Then you will have an idea of exactly what % you both put into the property.
Work out contents separately (as you will both want/need furniture/tv etc so will want to negotiate on this). Again, itemise and have a figure in mind for anything you bought together that you want to keep.
Figure out how much you would need to pay her to fairly to buy her out. Also work it out for yourself (as she may decide she wants to buy you out with help of family).. Same maths/numbers, just a different total.
Do the maths on costs of finishing mortgage early and selling (early redemption fees, estate agent costs, solicitor costs etc), Selling for x, paying off mortgage and all fees then splitting 66/33% (or however it works out based on both inputs above with decorating/upgrade spending).
This lets you see which often is best (financially) for you (each), and also lets you see how much not coming to an agreement and having to sell and split will cost.. It sometimes is a big gap, so paying her an extra 4-5k might sound a lot, but it might be much cheaper than having to sell.. Gotta spin the numbers!
Approach for a discussion. You may well find she has a counter offer in mind or disagrees on certain points (be prepared to concede. Worst case scenario you are selling.. See above!).
Don't let it turn into a fight, keep it factual and leave emotion at the door (very hard, I know!).
You may need a loan/borrow from family short term to pay her share.. Get a lodger in to help pay that back and help with the bills until everything has settled financially.. Really is a huge help!
Best of luck!