Associated Newspapers has claimed that its free daily, London Lite, is averaging 390,000 copies a day – within 10,000 of its 400,000-a-day target circulation.
And it says the Standard is so far only around 7,000 copies a day down as a result of the afternoon free newspaper war which erupted in the capital this month.
Rival daily thelondonpaper has yet to reveal a sales estimate.
Head of Associated Newspapers free newspapers division Steve Auckland said: "If you look at it now, it's not changed a lot since the first issue. There'll be subtle changes over the months but so far we're quite happy with what we've put together and once we get reader research back we'll obviously tweak it where we think we should.
"We're now hitting the 380,000 or 390,000 mark on a regular basis. I think our best one was 396,000 last Thursday.
"We're hovering between 389,000 and 396,000 on a print of about 405,000 – which is good going for us so far.
"If we find we've got ten thousand returns back from some areas we will tweak things around.
"The first thing we work out is have we got the merchandising right in [specific] areas? If we have got the merchandising right, have we put too many copies in one area, can we move it around elsewhere?
He added: "We're doing better than I thought we'd be doing at this stage. I thought we'd really be having to chase that figure, whereas we're getting that figure reasonably comfortably. We've been making sure we've become more efficient."