Bragg has criticised BBC programming before
The writer, broadcaster and peer was speaking at the launch of the 25th season of ITV's flagship arts programme, The South Bank Show, which he presents.
And he made a plea that BBC One bring back arts programming to prime time TV.
Lord Bragg said that BBC One, as the BBC's "standard bearer" TV channel, had an obligation to reflect the culture of the society.
'Think again'
"Proms attendances are going up and just try to get into the Tate Modern on a Saturday afternoon - but that is not reflected on BBC One," he said.
"I want to ask BBC One to think again, because it just won't do."
"This its major channel. This is for its largest tranche of viewers.
"This is where the biggest welt of the licence fee goes.
"Surely it can do better than that," he said.
Appeal
And he added that it was not acceptable to relegate the arts to BBC Two - or to the proposed digital arts and culture channel BBC Four, which may be approved by Culture Secretary Tessa Jowell on Thursday.
Lord Bragg appealed to BBC One controller Lorraine Heggessey: "I would say to Lorraine - it is not too difficult to pile on editions of EastEnders - why don't you make a real name for yourself by being the person who brings back arts documentaries?"
He said that while ITV had shown the South Bank Show 15 times since January, BBC One had shown only one arts documentary - which he described as less than a "fig leaf".
'Crucial audience'
A BBC spokesman disputed Bragg's description of BBC One: "We do not recognise Melvyn's headline grabbing vision of BBC One.
"Far from retreating from arts, BBC One this Autumn is moving them into prime time, with a special focus on that crucial audience, the family and children, who are of course the arts lovers of the future.
"Highlights include a brand new series on the impressionists with Rolf Harris, Omnibus specials on JK Rowling, Michael Bond and Jamie Bell, a hunt for the nation's favourite children's poem to mark National Poetry Day - and extensive coverage of this weekend's CBBC Proms In The Park."
The spokesman also said that ITV was not known for programming "arts programmes, or science or religious or natural history" in TV prime time.
It is not the first time that Lord Bragg has attacked British TV.
In 1999 he used the launch of LWT's autumn arts season to warn that British TV was in danger of becoming "moronic".