iCloud log in requires old phone number i neither have nor remember I recently got rid of my iPhone &amp; tried to log in via icloud on my laptop so I could get some contacts.

I know my Apple ID  &amp; my password well. However, on entering my credentials,  iCloud requires that I either enter my old number which I dont recall nor still posses.

Is there a work around for this? or am I doomed?
You have to start an account recovery here : https://iforgot.apple.com/password/verify/appleid

However, they may also ask you to verify your phone number and in this case, only Apple support can help you. They'll ask you question about your devices, your credit card and will ask you your new phone number.