Charlotte Church and former Crimewatch presenter Jacqui Hames have asked to be included in the inquiry into media ethics and phone hacking.
In a preliminary hearing for the Leveson Inquiry, David Sherborne, who represents a group of "victims", asked for the two celebrities to be added to the list of Core Participants (CPs) in the first stage of the probe.
He told the hearing, held at the High Court, that both had been victims of hacking by News Group Newspapers and other "media wrongdoing".
If the applications - which will be ruled on by Lord Justice Leveson at a later date - are successful, the total group of victims who are Core Participants in the inquiry will be 48.
The group, represented by Mr Sherborne, already includes actress Sienna Miller, PR guru Max Clifford, serving MPs, and Christopher Shipman, son of mass murderer Harold Shipman.
The first part of the inquiry will look at the culture, ethics and practices of the press and its relationship with the police and politicians.
Core participants for this part also include former MPs such as Lord Prescott and Mark Oaten, as well as football agent Sky Andrew and Coronation Street actress Shobna Gulati.
But Rebekah Brooks, former editor of The Sun, The News of the World and chief executive officer of News International, was refused the status by Lord Justice Leveson previously.
He said her involvement was more focused on the second part of the inquiry.
Today he also refused the status to Elaine Decoulos, who made an application in person during the hearing, saying she had been the victim of libel by newspapers in Scotland, England and the US.
Earlier today, Lord Leveson said oral evidence for the first part, which will be televised live, could start as early as next month.
He said: "The present thinking is, and I am not committing to this, that we are unable to be likely to start before the second week in November."
He told the hearing he originally wanted to press for a slightly earlier start, because of the "territory that has to be travelled before next summer".
The Leveson Inquiry, announced by David Cameron in July, aims to produce a report within a year.
Lord Justice Leveson said he was keen to "keep the focus" because the findings of the inquiry were likely to generate debate.
"A debate among the media, a debate among the political groups and a reconsideration of the way, perhaps, regulation or self-regulation, whatever comes out, is organised, which everybody is going to want to get on with.
"Which is why this part of the inquiry has to be before the normal timing which is when the police have finished whatever they want to do.
"It strikes me that the imperative is not merely a pressure to do what I have been asked to do, it is because it is actually very important to achieve something, broadly within from what is now about a year."
The inquiry was different from other probes generated by specific events such as the Hillsborough disaster, he said.
"The first problem is that a lot of precise detail which is normally the starting point for an inquiry is, or may be, tied up in the investigation being undertaken by police.
"Therefore to some extent, the inquiry puts the cart before the horse because if I were to wait for the police investigation it would not start in a time to be measured in not weeks, and not months, I don't know."
He said he would take advice from the Director of Public Prosecutions about how "far" he could go.
Lord Justice Leveson repeated assurances that the inquiry would be "open, transparent and fair".
The hearing was told some newspapers had produced material required for the inquiry on time, while others had requested extensions.
The issue of whether witnesses should be given advance warning of the areas of questioning they may be put under was also discussed.
Rhodri Davies QC, representing News International, said even some top executives might find the experience of giving evidence "daunting".
And Mukul Chawla QC, on behalf of Rebekah Brooks, asked if there could be some advanced warning of issues that may arise which were of "direct interest" to her.
Lord Justice Leveson said where possible if a direct interest was engaged, the inquiry would try to notify people.
He also said those who felt "particularly anxious or nervous" could be introduced through their own counsel to get used to talking in court.
"For some, the giving of evidence is indeed a difficult exercise and I will want to make that exercise as easy an experience as possible on the basis that this is not a trial, I am simply looking at a series of issues to obtain a series of recommendations.
"I am not unmindful of the pressures of giving evidence."
The first part of the inquiry, looking at the relationship between the press and the public, will also include a series of seminars, each chaired by one of the inquiry's assessors.
The first of these, on Thursday, will include brief presentations from people including former News of the World editor Phil Hall and Guardian editor Alan Rusbridger.
The seminars will also include open discussion from those attending the seminars, which includes a range of people from the media and members of various select committees.