Nonetheless, Parker welcomed the British move on consultation despite many unknowns.
"It is significant that in respect of their post EU relationship, they've said they want to start in negotiations with New Zealand, Australia and the US first," he said.
"There's lots of other countries that they could have chosen, but they have chosen us and that's good."
But negotiations could not begin in earnest until after Britain had left the EU in March.
This week New Zealand began talks in Brussels with the European Union for an FTA, although with 27 members, not counting Britain, the process is expected to take several years to complete.
Meanwhile, Parker is preparing to head to Mexico this weekend for a fifth round of free trade talks with the four members of the Pacific Alliance, Chile, Colombia, Peru and Mexico, which have a combined population of 220 million.
The talks began in July last year and the Alliance is also negotiating with Australia.
But because all of the Alliance members except Colombia are part of the CPTPP, New Zealand will almost certainly be expecting something more than has already been negotiated in that deal.
Parker said with a new Government in Chile, and recent elections in Colombia and Mexico, the meeting in Puerto Vallarta would be an opportunity to engage with new political leaders in the region.
"We see significant potential to promote integration within our region, demonstrate our shared commitment to free trade and reject the rising tide of trade protectionism in the world," he said.
After the meeting Parker will be heading to Mexico City to meet Mexican and New Zealand business representatives.
Mexico and Japan are the first two countries of six required to ratify the CPTPP before it enters into force. That is likely to happen later this year, or early next year.
Two- way trade with Britain is worth $2.9 billion – New Zealand exports $1.6 billion and imports $1.3 billion.
Two-way trade with the four Pacific Alliance countries is $1.8 billion - $722 million of exports and $455 million of imports.