* Move aimed to give govt more influence
* Inquiry has embarrassed govt/Murdoch
* Lively week upcoming with new witnesses
LONDON, May 4 (Reuters) - The British government will on Friday request it be allowed to see evidence at a high profile judicial inquiry into press standards before it is made public, recognition of how seriously the hearings have damaged the reputation of leading politicians.
In a sign that the government is seeking to achieve a greater degree of influence over the proceedings, it will ask to become "a core participant" in the Leveson inquiry, whose colourful question and answer sessions have already embarrassed at least one government minister and put News Corp proprietor Rupert Murdoch on the defensive.
Core participants have the right to see evidence before it is presented in court, can ask for evidence to be redacted and can pose questions to witnesses via the judge's senior counsel.
The government's intervention comes ahead of what is expected to be a lively week at the inquiry, with two former News of the World editors appearing to discuss their close friendships with Prime Minister David Cameron.
Cameron reluctantly ordered senior judge Brian Leveson to investigate the conduct and ethics of the press last year after the mass-selling News of the World admitted hacking into phones on an industrial scale to generate stories.
The investigation has since broadened out to examine the close ties between politicians, police and the media and whether these deterred the authorities from investigating the allegations of phone hacking when they first surfaced in 2006.
That in turn has shone a light on the influence of the salacious tabloid press, with critics arguing that a succession of governments have shaped their agenda to fit the political outlook of Murdoch and other proprietors.
Rupert and James Murdoch spent three days before the inquiry last week, while former Prime Ministers Tony Blair and Gordon Brown, and current leader Cameron, are expected in the coming weeks.
Cameron will face lengthy questioning over his friendship with former Murdoch executive Rebekah Brooks, who will herself appear before the inquiry next Friday to discuss her contacts with politicians during the period she edited the News of the World and the Sun tabloids.
He will also be asked about his decision to appoint a former News of the World editor Andy Coulson as his own spokesman, a move critics pounced on as a sign of Cameron's poor judgement and willingness to cosy up to Murdoch. Coulson will appear in court next Thursday.
Evidence presented at the inquiry has already increased the pressure on the government to be more forthcoming about its ties to Murdoch.
In some of the most damning testimony yet, emails released between James Murdoch and his top London lobbyist revealed how a ministerial aide had repeatedly sought to help Murdoch's News Corp in its controversial bid to buy BSkyB for $12 billion.
The admission forced the aide to resign and prompted the opposition to call for the minister himself to stand down, as his decision on whether to approve the deal, which would have been the biggest in News Corp's history, was supposed to be independent.
The tie-up was eventually pulled due to public outrage over phone hacking.
The Leveson inquiry will decide whether to grant the government's request at a special hearing on Friday afternoon.