They are called the "silver splitters", or grey divorcees. They are the baby boomers who have it all and still aren't happy, at least not together. As the divorce rate drops among other age groups, the rate of separations between couples in their 50s and 60s continues to rise. Not so much a seven-year itch as a 27- or 37-year one, the number of over-60s divorcing has risen by over a third in a decade.

While some suspect the disparity in the figures may be down to wealth – recession-hit younger couples cannot afford to separate, unlike older people whose children have left home and who have equity in their home – a report last week by the charity Relate warned of a looming crisis among older people, who are far more likely to be living alone than those from previous generations.

That is what is worrying Relate, which has produced data showing that people born in the postwar bubble between 1946 and 1964 will be the first generation for whom living alone in old age may be the norm, with all the troubling related issues of caring, loneliness and financial security. The number of over-60s getting divorced is rising each year, with a record 15,275 in 2011. This compares with 13,554 the year before and 10,273 a decade ago.

There is even an acronym for the children of these break-ups, "Acods" – adult children of divorce – who can find the break-up of their parents' marriage a challenge. Studies suggest adult children give more support to a widowed parent than to a divorced one.

Celebrities often don't help as role models. While Bill Nighy, 63, and Diana Quick, 66, separated after 27 years with such dignified silence that it took 18 months for it to be reported, John Cleese, 70, made it his business to bitterly complain about the settlement when he divorced his third wife, Faye Eichelberger, 64, after 16 years. He has since remarried. Jo Wood, 58, did a sterling job maintaining public dignity when Ronnie Wood, 66, left her for a teenager after 23 years of marriage

For the non-celebrity, non-loaded baby boomer, there is the added worry of a lonely future. "We're the baby-boomer generation, the first have-it-all generation; but we went at such a rate it was a challenge to know ourselves in among the busyness," said divorcee and therapist Jackie Walker, 53. "Sadly too many get stuck in their homes after divorce, especially women. Men can often trade in for a newer model but women tend to find that more difficult.

"The important thing is that I'm wholeheartedly sure that divorce can be a good thing. Why would you stay with someone just because you fear living alone? You both maybe can't stand each other and haven't for some time. It can lead to depression and anxiety when you are not connecting with someone.

"Divorce gets a bad press and marriage gets a hugely positive press, but frankly there's nothing more miserable than being lonely in a marriage. It's hideous, sharing a bed with someone you can't stand.

"If all the people who were miserable could become less miserable, what a nicer world we'd have.

"We have to help people feel less isolated and the best way is for people to learn to have a strong and stable relationship with themselves. So we've got more divorce and an amazing number of step families but that isn't necessarily a bad thing, nor is it necessarily the family that is born to you that will look after you in later life. We need to find new ways to form communities."

For Lorna, 62, a mother-of-two from Cheshire, divorce was something she never thought she could do. But her husband's looming retirement was the catalyst: "I couldn't have him around all the time; I knew that, you see, and he knew it. We surprised ourselves by singing from the same hymn sheet, so it was just the girls who were upset – they were upset that the house was sold, then they were angry at him later when he stuck the heels in over the pension, so we had to get the lawyers in.

"It turned the whole thing from strange to bitter. It was a pity that it got bitter. But then, as my daughter says, the marriage was bitter a lot of the time. You don't see it when you're in it sometimes, then the children leave and you're left with this chap. Well, that was how it felt to me.

"It is strange to be on my own. But I've nice neighbours and I've a nice flat and I was never frightened of being on my own like some people are. I haven't told my mother. She's 89 and of that generation where you didn't leave, you worked at it. Although I thought I was like that too – seems I'm not."

Bill Nighy And ex-wife Diana Quick, who recently split quietly after 27 years of marriage. Photograph: Mark Cuthbert/UK Press via Getty Images

Family lawyer Jonathan West says the approach of retirement is often a key factor in couples deciding to separate. "They realise there's nothing left to bind them together." The head of family and matrimonial law at law firm Prolegal, he has even conducted a divorce for a couple in their 80s. "People do try and hang on until the children have grown, then they think it's time for us, time for me. Finances aren't so stretched. It's a lot easier to divorce when you're older, without child support issues. A lot of clients will turn up with a grown-up child with them, as moral support."

Older couples will often spend a disproportionate amount of time arguing over something of sentimental rather than real value. "A collaborative agreement is always best" says West. "I think older couples are less inclined to go down the mediation or collaborative route, which is something that should change. Costs are always linked to the way a client conducts themselves."

For Nick, 70, from Birmingham, his wife's request for a divorce four years ago "knocked me for six". He struggled as a single man and lost friends he and his wife once shared. "Joining clubs was tough. Sometimes I'd pretend to be a widower – it was a bit too ripe to admit to divorce. But I'm getting there, even online dating!" However, he regrets not trying to save the marriage, and Relate is worried about the numbers of older people who do not seek help.

Only 14% of the couples it sees are over 50 and just 1% over 70. Chief executive Ruth Sutherland said couples needed to prepare to get old together: "Retiring is a good time to think about your relationship: is it ready for the changes that later life can bring? People often don't seek help until things are going badly wrong in their relationship and we're encouraging people to invest early to get the most out of their old age," she said.

Relate has launched an online relationship-checker to help. A key issue, says Relate, is that fractured families can result in less support for older people. Its research found that those who are married or living as a couple were more likely to be satisfied with life (82%) than those who are single, widowed, divorced or separated (71%).

"What this report shows us is that there are three pillars to a good later life – health, financial security and good personal relationships, yet relationships are largely missing from the wider debate around our ageing society," said Sutherland, who wants the government to introduce a minister of ageing. "We know from this report that good relationships have a direct impact on health and wellbeing, and that loneliness and isolation have negative impacts on both our health and wider society more generally.

"With one in five older people lacking the confidence to form new friendships and relationships, we are looking at a future in which 4 million people could be facing loneliness and isolation."

The report, Will you still love me when I'm 64?, was co-written with New Philanthropy Capital, a consultancy firm. Its chief executive, Dan Corry, said: "There are many pressures that growing older puts on relationships. People's identities change when they leave the workplace, declining health and shifting dynamics at home are all challenges. But with the right support, the evidence suggests that relationships can play a key role in making later life a positive experience for older people and also for society as a whole. We must see our ageing society as an opportunity rather than a drain on the public purse, but that means we need people to be supported to build and maintain a healthy network of relationships."

As Lorna prepares to go to a neighbour's barbecue, she mentions a quotation from the late, twice-divorced writer Nora Ephron, who spent a lot of time writing about divorce: "A good thing about divorce is that it makes clear something that marriage obscures – that you're on your own."

"That's true," says Lorna. "She also said something about being the heroine of your life, not the victim, and older people have just as much right to go for a spot of happiness as younger ones. I'm sorry for those who can't afford it, or are frightened, but I don't regret it."