The risk threshold – which determines whether a user is alerted and told to self-isolate – was lowered on Thursday, meaning more people are likely to be told to stay inside.
The Government said the decision was necessary to tackle rising infection rates by breaking chains of transmission.
It comes amid a growing debate over whether a national lockdown will be introduced to replace current regional restrictions.
But senior figures have told Boris Johnson it is becoming clear that the restrictions do not go far enough and warned that, at current infection rates, most of the country would be in maximum measures within a few weeks.
Jonathan Van-Tam, the deputy chief medical officer, told ministers the hospital admissions situation was now "very, very bleak" and he was beginning to change his mind about the benefits of local interventions.
The Telegraph understands that the Government is considering allowing a Christmas window in which families can meet, with lockdowns on either side of the festive period.
However, the technical changes to the NHS app – now downloaded by more than 19 million people, approximately 40 per cent of those with eligible phones – could send significantly enhanced numbers into de facto lockdown with no ministerial announcement.
Designers have also taken advantage of an upgrade to the Google/Apple technology that underpins the app to improve its ability to determine proximity between phones.
On top of improvements to the app’s ability to judge proximity, officials have lowered the risk threshold which determines whether an alert is sent from a score of 900 to one of 120.
A Department of Health spokesman said: "This is expected to increase the number of people asked to self-isolate by the app having been in close contact with someone who has tested positive.
"In the context of rising infection rates across the country, this change is necessary to break the chain of transmission, helping curb the spread of the virus and therefore ensuring fewer people are infected in the long term."
The Department of Health also said the problem of "ghost notifications" – a glitch that saw users informed they had been "exposed" but not instructed to self-isolate – had been resolved by the upgrade.
The new system also takes into account how infectious a person who tests positive was at the moment of contact, judged by closeness in time to the onset of symptoms.
It came as health officials told The Telegraph they are concerned that not enough people are coming forward for testing, meaning that the spread of transmission is not being tracked.
As of Tuesday there were 8,595 Covid patients in hospital in England, an increase of 37 per cent in seven days. The number of Covid patients on mechanical ventilators was 743, a weekly increase of 32 per cent.
New figures from NHS Test and Trace showed a 23 per cent increase in the number of positive cases in the week to October 21, with an 8.3 per cent positivity rate among everyone tested.