I am a UK national that has come to live in Spain during the transition period (1 February 2020 and 31 December 2020). Do I fall under the Withdrawal Agreement?

Yes. If you registered as a resident in Spain before 31 December 2020, you will be covered by the provisions of the Withdrawal Agreement and will be able to stay living in Spain legally and enjoying your rights as intended after the transition period has passed. 

In addition, if you didn't register as a resident before 2021, you can still benefit from the provisions of the Withdrawal Agreement if you provide proof of legal residence in Spain prior to 31 December 2020 when applying for residency. Those proof may consist of expense bills, rental contracts, employment contracts and any other document that provides factual evidence that you were living in Spain before the end of 2020.