"I apologise for that [delays]. There is a new system. I don't underestimate the personal frustration it causes to individuals...it is certainly not our desire to make it harder for NZers to come spend time in the UK. We love you there.
"New Zealand has one of the best, if not the best outside of the EU, visa regimes with the UK. Not all those places are taken up by young people - I'd love to see more young New Zealanders continue to come to the UK."
Almost as much comment was given to media on tomorrow's British & Irish Lions rugby test than trade.
Price gave only one potential sticking point on an FTA deal: "a big win by the All Blacks".
In June Britain appointed former New Zealand trade negotiator Crawford Falconer as its chief adviser on trade talks. Price was asked if Britain would sign-up any other Kiwi talent.
"Of course we have Warren Gatland at the moment and he is doing incredibly well...we know that Crawford will do just as well."
Britain and New Zealand have set up regular trade policy talks to push for greater trade liberalisation as Britain leaves the European Union. Britain cannot formally agree to any free trade deals until Brexit is complete. However, McClay said that would come around quickly.
"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.
Price said he believed a deal could be struck "as soon as we Brexit".
On the prospect of opposition from British farmers worried about competing against New Zealand producers, Price said he was at the supermarket chain Waitrose for a decade before taking his current job.
"And I'm very pleased to say we took on New Zealand lamb, it was fantastic.
"There's a lot [of trade] that already exists...what you find when you move to politics out of business is that there are lots of people that have a voice. So expecting all 65 million people in the UK to agree with everything...won't happen.
"What I believe, though, is the UK has a great opportunity going forward to be a free-trader with the whole of the world."