From Longman Dictionary of Contemporary Englishfinish up phrasal verb1 British English informalEVENTUALLY to arrive at a particular place, after going to other places first SYN end up I took a long holiday in Italy and finished up in Rome.2 British English informal to get into a particular state or situation as the result of what you have done, especially without planning or expecting it SYN end up He tried to bribe a police officer and finished up in jail. with Brett got into a fight and finished up with a broken wrist.3 finish something ↔ upEATFINISH/USE ALL OF something to eat or drink all the rest of something, so there is none left Come on, finish up your drinks! → finish→ See Verb table
Examples from the Corpus
finish with• From his original £30,000, the client had finished up with around £000.• Wash it all down with a Kirin Ichiban and finish up with green-tea ice cream.• After mitosis it is in general essential that each daughter cell finishes up with the right number of chromosomes.• The top end finishes up with the three-over-two layout of Gotoh black chrome machines. 