The Progressive Patriot, by Billy Bragg (BANTAM £17.99 (296pp) £16.50 (free p&p) from 0870 079 8897); On Royalty, by Jeremy Paxman (VIKING £20 (370pp) £18 (free p&p) from 0870 079 8897)

Barking or Balmoral?

Memoirs from the rock 'n' roll frontline are usually anecdotal affairs, cobbling together tour reminiscences, high jinks with sex'n'drugs, and celebrity hobnobbing. Not so Billy Bragg's The Progressive Patriot. Following his last album, England, Half-English, the self-styled "Bard of Barking" has put down his guitar in the latest chapter of his mission to reclaim English patriotism. By turns charming and engaging, aggravating and exasperating, his book mixes the archaeology of Barking, family lore, the influence of traditional English ballads on Simon and Garfunkel and Bob Dylan, 17th-century political history, seeing The Clash for the first time, and the importance of football.

An earnest endeavour drives all this forward, even if some parts read like a student manifesto. Bragg wants to be able to celebrate Englishness without any taint of fascism or racial prejudice, celebrating our "collectivist heritage". His version of English history is one of rebellion, strikes and the rise of the disenfranchised, and he ties his own family history into these events. He also writes movingly of the first time he heard "Scarborough Fair". It was an epiphany: "My feelings were no doubt greatly enhanced by the fact that the song was in the Dorian mode, the melancholy musical scale of medieval plainchant", connecting it in the fledgling Bragg's imagination with the ruins of Barking Abbey. Elsewhere, he is rather less mystical, and writes keenly on the politics of punk and the formation of Rock Against Racism, seeing these movements as part of an ongoing struggle to win equality and emancipation.

The Progressive Patriot overflows with integrity and commitment, but is also an immensely frustrating read. Bragg avoids the real politics of English identity - an identity eroded by New Labour. He is hypersensitive to right-wing extremism, and with disappointing predictability records the association in the 1970s of the Union Jack with the National Front. Frankly, if those on the left had prevented the far right setting the agenda and reclaimed the flag (as they did with the DM boot and skinhead haircut), they wouldn't have such kneejerk reactions against it, and the cross of St George, today.

There are other straw men that Bragg likes knocking over. He has a go at British values, arguing they are never defined in arguments about multiculturalism. Yet within a couple of pages he has found those very values in a Daily Telegraph poll revealing that free speech, the defiance of Nazi Germany, and fairness and fair play are the most commonly stated national characteristics. But he still can't resist attacking "traditionalists" for their dodgy opinions. And for all his dismissal of top-dog, kings-and-queens history, Bragg has a surprising amount to say about Charles I and the succession in arguing for a Declaration of Rights.

There are reasons why the monarchy is important to national identity, and these are examined in typically pungent fashion by Jeremy Paxman. Paxman also has a lot to say about Charles I, devoting a chapter to a vivid retelling of his execution in 1649. But On Royalty is really more concerned with the royal family today - its standing, its relevance, its future - and with the fascination it exerts on the public imagination.

Paxman, a declared republican, is not immune to the charms of the royals. He describes a lunchtime tête-à-tête with Princess Diana and staying at Sandringham as a guest of Prince Charles. He blusters into a room, nearly speaks to the Queen, but then blusters out, overcome with nerves. He relishes the foibles of monarchs, from the grotesque attempts of Carlos II of Spain to father an heir, to Farouk of Egypt - a "pampered, kleptomaniac lard mountain".

Paxo has great fun with these figures, in a pugnacious and abrasive attack. Yet there is also a thread of humanity running through his account - a certain sympathy for those victims of pomp and circumstance. The lottery of hereditary succession means that there but for the grace of God could go any one of us.

On the face of it, then, the theoretical case for the monarchy today looks pretty feeble. We don't have hereditary brain surgeons, and (alluding to Thomas Carlyle), "In a system in which the king wielded real power, he really ought to be the wisest man in the country". Quite. The Queen, however, has merely the trappings of power, and this tends to undermine serious calls to abolish the monarchy. Moreover, as the power of the Prime Minister continues to grow, it seems reasonable to have some non-party personage remaining vigilant. The Queen may be the dog that never barked but, at least theoretically, she could.

Are there serious alternatives? The appointment of a president, and all the bureaucratic paraphernalia of such an office, would do away with the centuries of practical constitutional evolution integral to British culture. To put it bluntly, it wouldn't be "British". As Paxo declares, "Politicians spend their lives attempting to make a mark upon history. Kings and queens embody history."

The biggest problem the monarchy has to face is from Paxman's own quarter: the fourth estate. The 1969 BBC documentary The Royal Family was the consequence of a desire to secularise the monarchy, showing it as a functioning family. Now, 40 years down the line, this has created impossible conditions in which the privacy of the royals is spectacularly compromised. Paxman is at pains to point out that the press has never been consistently loyal, and was arguably worse in the past. The death of George IV was reported in The Times (1830) by remarking that he was "fat, frivolous, grotesque, selfish, lazy, vain, lecherous, spendthrift, corrupt and essentially worthless".

Ironically, a reluctant acceptance of the status quo pervades Paxman's bracing investigation. The Queen helps to define the identity of her people by being their servant; she performs visits that provide no discernible benefit to her. Yet the lesson of history is that royal families survive under the indulgence of the people, which if the mood prevailed could remove them "bloodlessly" (as in 1688) or not (as in 1649). But, as Paxman brusquely concludes, why bother? The system works, and the last thing we need is a Declaration of Rights written by a pop star.

Nick Groom's 'The Union Jack' is published by Atlantic