Meanwhile, Labour said leaked documents showed passengers on private jets were able to enter the UK without being seen by border officials, raising fears among staff that security was being compromised.
One UK Border Agency official complained to managers about not even being "allowed to physically see the passengers", saying it was "at odds with national policy" and "is creating an unnecessary gap in border security", the emails showed.
Government estimates show there are between 80,000 and 90,000 private jet flights every year.
Further leaked emails showed Mrs May's pilot scheme to relax border controls - referred to as level two checks - was used 260 times in the sixth week of the trial, the week ending 16 September.
This compared with 100 times in its first week and 165 in week nine, ending 9 October.
Shadow home secretary Yvette Cooper said the the new information about the scale of the "borders fiasco" was "startling".
"The home secretary has to release these facts and figures immediately. As long as she refuses to do so, and keeps running away from media interviews, people will think she has something to hide.
"We have warned for some time that the government's chaotic approach and the scale of border agency cuts risked weakening our borders.
"The home secretary needs to show she has a grip on what is going on at our borders and is capable of sorting this fiasco out rather than making it worse," she said.