"If you are going to have any successful negotiation, you have got to have a fall-back position, which the other side understands and believes is credible," King said in a BBC radio interview to mark 10 years since the start of the global financial crisis.
Britain is due to leave the EU in March 2019 and began its formal exit talks in June.
Initial areas of disagreement include Britain's financial liabilities, the rights of EU citizens already living in Britain, and border arrangements between the British province of Northern Ireland and the Irish Republic, an EU member.
If Britain fails to reach a deal, trade would be governed by the World Trade Organization, which allows both sides to impose import tariffs and customs checks, and does not replicate existing agreements on sectors such as airlines and financial services.
On Thursday King's successor as BoE governor, Mark Carney, said Brexit worries were weighing on business investment and pay decisions, and that sterling's fall since the June 2016 Brexit vote was to blame for above-target inflation.