I think for a start they could televise the lobby briefings. There's nothing magical about them and I think people might find them a bit dull, but "Downing Street sources" usually means the journalist was sat in a briefing room being fed the line from the press -- the Prime Minister's spokesman. We can just put it on TV and see that.
The access -- I think it's unhealthy full stop to have lobby terms. Journalists shouldn't accept anonymous briefing from the Prime Minister's spokesman or from other players because most of the time it's used by politicians to besmirch other politicians without getting their fingerprints on it.