Thanks for your question.
It all turns on whether you intended it as a gift or paid the money for the car in the expectation that it would be paid back at a later date. From the wording of your post it appears as if it was a simple gift from you to her as a loving couple and therefore you would not be able to sue her to recover the monies.
It it was made plain that she should pay you back the money over a period of time, or that the car was hers only for the period in which you were in a relationship but upon the relationship ceasing it was to be returned to you, then you may be able to sue to recover the monies. Your case here would be stronger if you had documentary evidence of the intended arrangement but you could still issue if you did not, although the reality is that your realistic chances of success would decrease.
If you consider that she has obtained this by deception because of the short period of time between your break up then this conceivably an offence under the Theft Act 1968, although there may be difficulties if you did not actually buy the car. You could use this as leverage and possibly speak to the police to see if they consider it obtaining property by deception.
If the above does not apply then, regrettably, she is under no duty to pay you the money and you may benefit from adopting a less adversarial approach and appealing to her sense of fairness to come to a compromise to either give you some money now or at a defined later date (or repayment plan). Get this in writing.
Sorry it could not be better news, the fact that no couple in a relationship considers these things is not lost on me.
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