Peters blamed the UK's 47-year membership of the EU for it not being ready to pursue multiple trade deals around the world at once.
The European Commission negotiates trade deals on behalf of the whole bloc, which means the UK has not negotiated a trade deal since it joined the forerunner of the EU in 1973.
New Zealand, which is also in formal trade negotiations with the EU, negotiates its own trade agreements rather than as a bloc with other countries.
Peters said: "We've had to look offshore for a long time and so we are seriously match fit when it comes to that, in a way that I don't believe that the UK is because the UK has been locked up in the EU all these years.
"In terms of their trading skills and finesse and their firepower – without being critical – they've never had an outing lately."
The deputy prime minister added: "They've never had a test, so to speak. It's like coming into an Ashes contest when you haven't played for 30 years – it's the same thing in the UK when it comes to this.
"Here we are out here in the South Pacific, ourselves and Australia, and we believe we're totally match fit and ready to go."
British officials want to get as many trade agreements finished before the end of the transition period at the end of the year in order to show that post-Brexit "Global Britain" can be a success.
Once transition finishes at the end of the year, the UK will fall out of the EU's trade deals with countries such as Japan.
Failure to agree a trade deal with the EU and rollover agreements with countries that have EU trade deals will mean the UK trading with them on less lucrative WTO terms, which involve quotas and tariffs.
Peters' comments come after it emerged talks on a UK-Japan trade deal had hit a snag over the treatment of Stilton cheese following hopes that an agreement could be clinched last week.
The Department for International Trade said talks with the US would continue "at pace" after the third round of trade talks ended. The US does not have a trade deal with the EU.
While Britain can negotiate trade agreements during transition, which began after Brexit on January 31, the deals cannot take effect until the UK has left the EU's Single Market and Customs Union on December 31.
A second round of trade talks with New Zealand is planned for October after initial negotiations in July.