The brothers are estimated to be worth £6 billion. Richard Desmond, the chairman and owner of Northern & Shell, who just sold Channel 5 for £450 million, follows them in second place.
Martin Sorrell, the chief executive of WPP, appears at number 11 in this group, and number 362 in The Sunday Times list of the richest people in Britain.
Nick Robertson, the founder of Asos, is given a honorary slot in the list as a former Carat media buyer.
1) Sir David and Sir Frederick Barclay (16 in Sunday Times Rich List)
Worth £6 billion (£2.35 billion in 2013)
Owners of Telegraph newspapers, as well as property and online retail businesses.
2) Richard Desmond (78 in Sunday Times Rich List)
Worth £1.2 billion (£860 million in 2013)
Desmond, who owns the Express Newspapers-owner Northern & Shell, just agreed to sell Channel 5 to Viacom for £450 million, so could rise up the rankings next year.
3) Mark Getty and family (155 in Sunday Times Rich List)
Worth £650 million (£650 million in 2013)
Oil empire descendents and part-owners of the Getty Images picture agency, in which they sold a majority stake to private equity company Carlyle in 2012.
4) Jean-Francois Decaux (joint 199 in Sunday Times Rich List)
Worth £500 million (new entry)
Son of Jean-Claude, the founder of outdoor advertising company JCDecaux, and recently relocated to London to run the British operation. The total wealth of the Decauxs is £3.3 billion, according to Forbes.
5) Felix Dennis (joint 199 in Sunday Times Rich List)
Worth £500 million (£473 million in 2013)
Owner of Dennis Publishing, which includes The Week and Auto Express. Dennis is a successful poet and is working to create a new forest, the Heart of England, in Warwickshire.
6) Nick Roberson (235 in Sunday Times Rich List)
Worth £448 million (£278 million in 2013)
Since leaving media (he was a media buyer at Carat and Young & Rubicam) Robertson has done well. His online fashion business Asos, has grown into a formidable operation, in which he has a £389 million holding.
7) Mike Danson (245 in Sunday Times Rich List)
Worth £412 million (£376 million in 2013)
Runs Progressive Digital Media, which owns the New Statesman. He also founded the market research business Datamonitor and sold it in 2007 for £502 million.
8) Cristina Stenbeck (joint 259 in Sunday Times Rich List)
Worth £376 million (£405 million in 2013)
Leads the Swedish-based company Kinnevik, which owns the Metro newspapers. She took charge after her father died in 2002, aged 59.
9) Lord Heseltine and family (337 in Sunday Times Rich List)
Worth £278 million (£264 million in 2013)
Heseltine, 81, a former deputy prime minister, founded Haymarket Media Group which is run by his son, Rupert, the chairman, and the chief executive, Kevin Costello
10) Elizabeth Murdoch and Matthew Freud (joint 353 in Sunday Times Rich List)
Worth £260 million (£255 million in 2013)
Murdoch founded the TV production company Shine, which was sold to News Corporation, the company run by her father Rupert as chairman and chief executive, in 2011. She continues to run the business as the founder and chairman.
11) Sir Martin Sorrell (362 in Sunday Times Rich List)
Worth £257 million (£210 million in 2013)
The chief executive of WPP is now likely to be the leader of the world’s largest advertising group for a while yet, following the merger between his two rivals Omnicom and Publicis falling through earlier this month.
12) Jamie Oliver (joint 396 in Sunday Times Rich List)
Worth £240 million (£150 million in 2013)
Oliver can now be considered a fully-fledged media owner, as the second biggest book publisher in Britain after J K Rowling, the brand behind a YouTube channel with more than a million subscribers and the face of numerous advertising deals.
13) Jonathan Klein (joint 458 in Sunday Times Rich List)
Worth £200 million (£200 million in 2013)
Founded Getty Images with oil heir Mark Getty. The photograph company was taken over in 2008 in a £1.2 billion private equity deal.
14) Lord and Charles Saatchi (joint 647 in Sunday Times Rich List)
Worth £140 million (£135 million in 2013)
The brothers who founded Saatchi & Saatchi then left in 1995 to start M&C Saatchi. Maurice still has a stake in M&C Saatchi, but Charles sold his for £4 million.
15) Mike Luckwell (joint 666 in Sunday Times Rich List)
Worth £135 million (£135 million in 2013)
Luckwell is a media entrepreneur and bought Reader’s Digest in February for just £1. He plans to relaunch it.
16) Sir Ray Tindle (joint 691 in Sunday Times Rich List)
Worth £130 million (£130 million in 2013)
Owns Press Holdings, a £100 million local publisher that has 220 newspaper titles in the UK.
17) Michael Green (joint 813 in Sunday Times Rich List)
Worth £110 million (£105 million in 2013)
Green built the TV company Carlton into a big hitter, before being ousted in 2003.