Johnson will use the majority he won in Thursday's election to forbid any extension of the Brexit transition beyond 2020, leaving him less than 11 months to strike a comprehensive trade deal.
The British currency fell 1.2% to $1.3155 and to 84.59 pence against the euro.
After the United Kingdom leaves the EU on Jan. 31, it enters a transition period in which it remains an EU member in all but name while both sides try to strike an agreement on their post-Brexit relationship.
The latest reports came as a surprise. Some investors had thought that Johnson would use his majority in Parliament to adopt a more moderate approach towards Brexit negotiations.
Analysts say a comprehensive trade deal with the European Union could take years, not months, to negotiate and the kind of hard deadline Johnson is aiming for would make it difficult for negotiators and provide a fresh source of uncertainty.
That raises the possibility of either a "bare-bones Brexit" more or less on WTO terms or yet another cliff-hanger next December, said Marshall Gittler, chief strategist at FX analysis firm ACLS Global.
A business survey on Monday showed British businesses endured their worst downturn since mid-2016, before the election. Unemployment data is due shortly.