English's submission was made before May called for a snap election on June 8 - less than a year after Britain voted to leave the EU. May took office in July after a Conservative Party leadership race following former British Prime Minister David Cameron's resignation.
English and May met at 10 Downing Street in January and spent 90 minutes talking over a lunch. They emerged with warm words about the long relationship between the two countries.
While Britain can't enter any free trade agreements until it has left the EU - something that will take at least two years - both leaders made it clear New Zealand would be among the first.
However, asked if she had any intention of improving access for New Zealanders after presiding over a tightening of the rules in the past few years, May was unapologetic.
She said most visa applications from New Zealanders were approved and schemes like the two-year visas under the Youth Mobility Scheme gave opportunities to live in the UK. At the time, English described May as "engaging".
"She listens carefully, a very determined woman and a clear thinker. I was left with the impression these are the kind of qualities you need, the UK needs, to get through what is going to be a complex process."