Bridget McConnell looks troubled when our conversation turns to the Leveson Inquiry into the Murdoch book of misrule.

For her, hackgate is not an abstract concept but one that affects her – and her children – directly.

"One of the things that has really struck me about the emerging evidence is that we always presumed our privacy didn't exist. Isn't it terrible that we normalised that?" She is referring to those years between 2001 and 2007 when her husband was First Minister. At present the couple are in legal dispute with a neighbour in Stirling over use of a coal shed, but of more national concern is the police information that Jack McConnell's name and phone numbers, and those of the couple's children Hannah and Mark, have been found in the notes of the private detective Glenn Mulcaire who worked for the now defunct News of the World. As a result, Lord McConnell, who became a life peer in 2010, has now joined the thousands of potential victims seeking legal redress against News International. Phone hacking – covertly accessing people's voicemails – is a criminal offence.

In truth, though, Bridget McConnell is more comfortable talking about the zest and zing of Glasgow's creative edginess and legacy of treasures which bring increasing numbers of visitors and international commentators to the city. She rattles off a list of accomplishments achieved in the first five years of Glasgow Life, the independent charity which she leads as chief executive and which, on behalf of the city council, is charged with helping to improve lives through world-class culture and sport. Credited with being the key mover behind the restoration of Kelvingrove Art Gallery and Museum – which reopened in 2008 – she refers to its present retrospective of Italian art, The Essence of Beauty, as an outstanding example of the city's riches. "Where else could you walk into a civic collection and see works by Bellini, Botticelli, Filippino Lippi and Titian?"

But it is her earlier use of that word "normalised" in relation to phone hacking which grabs the listener's attention because of its disturbing implications. These days no public figure is naive enough to think the media will regard his or her private life as sacrosanct. Even so, many folk will share Bridget McConnell's shock at how accepting we have become of tabloid prurience and its pernicious masquerade as the public's right to know.

"The job I do is an incredible privilege," she says. "I can't think of a more exciting one anywhere in the UK. But – and I'm certainly not looking for sympathy – there have been consequences on a personal level, and the biggest is my sadness that my children never want to live in Scotland again." At the heart of that drastic disclosure are the various furies which have flared around the McConnells during their high-profile careers. Her first lesson in keeping cool under fire came in 1998 when her appointment as Glasgow's leisure and sport supremo was attacked by some as blatant Labour cronyism. (Jack was a former general secretary of the party in Scotland). But the accusation ignored the fact that Bridget, as community service manager for Fife, was already considered among the most effective and imaginative social administrators in Britain; someone to drive forward the new, expanding world of information technology in a spirit of inclusiveness.

Some time later, as her husband was bidding to become Scotland's third First Minister, the furies struck again when he admitted that seven years previously he had been involved in an extra-marital affair. Anyone who witnessed the resulting press conference couldn't have failed to have been impressed by Bridget's unwavering dignity as she appeared by her husband's side. In a statement the couple expressed their thanks to their family and "trusted" friends who had supported them in resolving the crisis in their marriage. Very publicly the skeleton was laid to rest.

But this recent information from Scotland Yard suggests that their phones might have been hacked during Jack McConnell's two terms as First Minister when his son was a university student and his daughter just beginning a new job. It is the possibility that Hannah and Mark's private lives were violated that the McConnells find most painful and intolerable.

"It's not that my children have a huge dislike of Scotland but I know they'll never want to live or work here again." From their perspective, she says, the country is a goldfish bowl where anyone linked to somebody with a public role is always under terrible scrutiny. Hannah, now 33 and married with two young children, works for the British Council in London; Mark, aged 29, is an English teacher in Dubai.

Bridget believes her son restricted his social life after the media homed in on a foolish prank involving two of his friends at Bute House, the First Minister's official residence in Edinburgh. Larking about in dressing gowns, and swigging alcohol from a bottle, the lads put the episode on YouTube whereupon it ended up all over the papers. "When I look back I can see that Mark, either consciously or subconsciously, limited engaging with friends after that. It was such a one-off, the kind of thing teenagers do, and actually he was sleeping in bed at the time. But I think that was the period which probably left him with unhappy memories about living Scotland."

Meanwhile Bridget was taking on the ambitious challenge of establishing Glasgow Life as a charitable organisation which would thus exempt it from VAT. Audited figures show that as a result of that status, the enterprise – with 2800 staff across 154 venues from libraries to swimming pools – has achieved savings for the city of £53.3 million in these five years, savings which have been spent on frontline services across the city. And now in its first year, the Riverside Museum has attracted 1.3 million visitors, more than double its initial target. The final cost of that project, which includes the Glasgow Museums Resource Centre at Nitshill, and wider infrastructure and regeneration works is £100 million but the actual Riverside building was completed at a cost of £74 million. Reflecting the kudos of such ventures, the New York Times recently rated Glasgow as 12th on its list of "must see" destinations ahead of Florence, Vienna and the Maldives.

Whatever the outcome for the McConnells of Scotland Yard's hacking investigations, Bridget certainly won't allow it to distract her from Glasgow 2014, that red letter date when the city's east end hosts the Commonwealth Games. But why stop at 2014? No reason at all, which is why her teams are already working on a presentation for the 2018 Youth Olympics, Glasgow being the only UK city selected to bid for the event.

But given our economic gloom, how confident can she be that 2014 will meet the proud claim that the games will radically transform that area of Glasgow where poor health is endemic and unemployment, in some cases, stretches back four generations? "The games won't just be about buildings and athletes, the demi-gods among us. They'll also be about a lifestyle legacy for folk who have, perhaps, felt excluded from civic society before. The indoor arena and velodrome aren't just world class but have been built with the community in mind. That's why we're working with the Glasgow Regeneration Agency and the health board to encourage local people to feel confident in themselves about applying for the jobs created in a very exciting place."

Sceptics insist such ambition requires a miracle worker, but Bridget McConnell has learned to have more faith in human nature. Some years ago on the launch day of Glasgow's free admission to municipal swimming pools for children between five and 18, she remembers thinking that if the take-up was disappointing, her teams' hard work on the project would have been for nothing. That morning she toured the baths with a colleague. At Easterhouse two little girls, aged about six, arrived hand-in-hand and emerged from the changing rooms with their bathing suits over their pants and vests.

"They'd never been to a swimming pool before but the staff reacted beautifully. They didn't make them feel silly but unobtrusively showed them what to do. And when the one-hour session finished those wee friends dried themselves, put on their clothes and ran out to join the long queue of kids all over again, thrilled by what they'd achieved."

Despite the city's financial pressures, that free facility remains, and for Bridget McConnell that day symbolises something simple but profound: the sheer delight of witnessing a bright idea made good.