"We can make a lot of progress, we just can't negotiate until Brexit is over. But that's only 18 months away, it will go by very quickly," McClay said.
"You might remember earlier this year the Trade Secretary Liam Fox confirmed that New Zealand, along with Australia, would be first cab off the rank to do their new FTAs when they are able to.
"But we are a small country a long way from everywhere - we need to keep reminding people of our relevance so it is a good opportunity."
In June Britain appointed former New Zealand trade negotiator Crawford Falconer as its chief adviser on trade talks.
McClay said that was "excellent news for us".
"He's a free-trader, he helped design the New Zealand trade model. I do think that's a signal they want to be closer to New Zealand on the liberalisation spectrum than some other countries.
"I'll be saying to Lord Price that New Zealanders do have expectations that we will get a really good deal that will send a signal to the world that the UK and NZ will continue to be friends and work together."
McClay acknowledged many British farmers would be opposed to a comprehensive deal with New Zealand.
"My message to the Welsh lamb farmers...is that their lambs are as good as ours...the world is a big place, they should be...looking further afield to Asia and the Middle East. I don't think they have much to fear from us."