It is now 50 years since Dervla Murphy published Full Tilt, her account of a bicycle ride from Ireland to India.

She has continued to journey and to write, about Tibet, Nepal, Ethiopia (with a mule), India, Baltistan, across South America, Africa and Madagascar, often in danger, but rarely if ever self-dramatising. The doughtiness extended to her private life. Bringing up a child as an unmarried mother in 1970s Ireland (after a relationship with the journalist Terence de Vere White) was no picnic either. Somewhere around the middle of her writing life, and interestingly after the publication of an autobiography Wheels Within Wheels that suggested her journeying might be tailing off, a new political edge began to creep into the work, starting on different frequencies with the political situation in her home country but also in her investigation of "the nuclear stakes", Race To The Finish.

In recent years, despite fresh travels to Cameroon, Rwanda, South Africa, Laos, Cuba - itinerary lists are unavoidable but also slightly beside the point - her attention has been taken by the fate of that assassinated placename, Palestine. Between River And Sea reflects on a three-month visit to Israel in 2008, with five months spent on the West Bank over the next two years. It has already been leapfrogged by the widely admired A Month By The Sea, which describes a summer 2011 visit to Gaza. The story the present book tells is necessarily less savagely dramatic and also more complex.

It's easy, given all the pins on her personal globe, to miss the point that all the strings go back to one place. An Irish passport makes for an easier introduction in the region than a British or US one. And there are a couple of moments of presumed solidarity, as when Murphy is asked about how it feels to be occupied by the British Army, which may be an individual's naivety or may be an insight into al'Jazeera news values. She remembers the creation of Israel as another 20th-century wilderness of mirrors. "Pre-partition, as a juvenile Irish nationalist with rabid tendencies, I admired the anti-British Zionist militias and scorned as 'traitors' any Irishmen serving with the Palestine Police. However by 1947 [i.e. age 16!] I had left the rabid stage behind and confusion was setting in."

That confusion, innocence or occasional ignorance of the facts is what drives Between River And Sea, but there is another strong connection to Ireland. Much was said during the Irish Troubles about the "breakdown of law and order", a phrase which, along with "men of violence", led mainland Brits to imagine a country whose consensual desire for peace was marred by youths throwing rocks and their fathers and uncles caching guns and bombs.

The reality was that law and order in Ireland broke down at a more profound level. Civil obedience collapsed in a thousand small ways and Irish men and women were set against one another at every level of daily engagement, whether parking a car or buying a house. That same reflex fractiousness defines life in Israel and Palestine today, as any visitor will tell you. Strangers are ignored. Requests for directions are snapped at. Outsiders are blanked by the ultra-Orthodox, who have acquired an unnerving ability to make you feel invisible. A chance remark, or mere mention of a name, can end a promisingly amicable conversation in a split second, never to recover. Native-born Israelis cherish their "Sabra" (prickly pear) reputation.

Going up the scale, it is hard to imagine how brutally contentious politics in the region have become, and how intellectually bankrupt. Endless checkpoints, bureaucratic delay, a thousand pinprick irritations keep the Palestinian population in a state of permanent anxiety and non-specific dread. Insomnia is endemic; irritability almost the default position.

The iniquities of West Bank settlement and Palestinian dispossession have been extensively documented before, by Edward Said, Raja Shehadeh and others, but no one has given such an affecting account of how it feels, day by day, to live in this environment; and ironically it is the normalisation of repression, its quotidian banality, that allows the big crimes to pass unremarked. The Oslo accords have not, for example, been published in Arabic, lest anyone recognise just how big a sell-out they were. Avigdor Lieberman's Yisrael Beiteinu preaches a Final Solution to the Palestinian 'problem'. Gangs of uncircumcised Jews or faux-Jews from the old Soviet bloc practise a kind of entrepreneurial genocide, unmolested by the authorities.

This is the land where, as Shehadeh reminded us, Jew, Christian and Muslims of different tendencies once lived peacefully under the Ottoman Empire, sharing common language-roots as People of the Book. Tiny chords of that harmony can still be found. The almost unvisited Chapel/Mosque of the Ascension in Jerusalem, built on the spot where Jesus is supposed to have risen into heaven, sees both Christian and Muslim observance and is looked after peacefully by both communities. I've been there, but whether it's the saddest place on Earth or the most hopeful, I can't quite tell, and Murphy comes to no conclusion.

She does on the big question, though, suggesting that the only way out of the current morass is a One-State Solution in which Jews, Palestinians and all other groups join in a hyphenate nation run on one-man, one-vote. Unfortunately, the optimism seems desperate rather than earned or proven. It might work in Ireland. It's a stretch to see it working in a 'Holy Land' which is now sick rather than sacred.