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The transfer is not dated or effected therefore arguably she can change her mind. The fact that she has expressed on number of occasions that she does not want to proceed, you should not proceed with the transfer until she agrees. As you are not married, you are right, there shall not be any settlement agreement. She will only be entitled to the 2% she owns, that is all.
The best way forward would be for her to seek independent legal advice. It appears that she is refusing to proceed with the transfer because she thinks she is entitled to more. However, this is not the case. If she seeks legal advise a solicitor can advise her on her position and help her make an informed decision. I hope this helps.
Please kindly confirm whether you require any further assistance.
She may have a small share in the property, but this does not effect her right to withdraw her consent particularly since the TR1 is not dated. The fact that you are not married and there shall be no settlement, again, this does effect her right to the property and nor her decision to withhold the transfer.
You can apply to the Land Registry. However, I do not suggest you to do so as she has clearly withdrawn her consent/ decision to proceed with the Transfer.
You can apply to the Court for an order for sale. However, this option can be quite costly.
Please confirm whether i have answered your query.