Put yourself in her shoes as well when you think about it.
Shes supposedly in a proper relationship, if its long term (in both your minds) shes probably thinking he could just say move out, at any time and is faking it.
Shes probably a bit nervous because of this.
She is showing commitment, if your refusing to let her take a stake then in effect your doing the opposite.
Saying that, right now, her best bet is invest it (even savings) and wait till either rates drop or you move. Seems pointless to pay off a lower rate. (Stick £20k in an ISA)
Or an alternate approach is. You agree to sign over a share of the house to her (with provision that should you split you can repay her). She gives YOU the £45k and you invest it.
That way you still have the cash to repay her, shes got her stake and feels bought in, you arent paying down low cost debt when investing/saving would be better.
If you seriously think shes a keeper then that seems to tick all the boxes.