It’s the middle of the night and the baby is screaming again. It could be hunger, teething, wind, divine retribution, or the seagulls laughing outside the window. You no longer know because you are so tired you consider blinking to be rest. What do you do? Feed and rock her back to sleep? Leave her to cry it out? Visit her at intervals to make manic shushing sounds? Or stay up all night consuming the millions of books and online tutorials that now exist on sleep training, which, in terms of controversial industries riddled with conflicting advice for parents, is basically the new breastfeeding?

For the knackered parents who can afford it, the answer might be to call in a consultant. Firms such as London-based Infant Sleep Consultants have created a new industry out of advising parents on how to train their baby. Sleep training packages include Skype consultations for £180, three-hour home visits for £250, overnight stays for £390, and 24-hour support for £620.

“We get called in because everything has gone wrong and it’s our job to fix it,” says Annie Simpson, a former maternity nurse and mother of three children. “By the time they contact us they are desperate. Our clients are highly educated people. They have read extensively, tried a multitude of things, and nothing has worked.”

So what does work? “We give them the support and confidence to fix things,” Simpson replies. “We talk a lot about putting babies to bed drowsy but awake. I don’t believe in cry-it-out. It’s not a method we advocate.” And co-sleeping? “If it’s working then go for it.”

For Andrea Grace, the UK’s longest-standing children’s sleep trainer who set up independent practice in 1998, the rise in private sleep-training services can be explained by the pressures on professional couples. “They don’t tend to have their families around them, they both tend to work, and they have to do everything,” she tells me. “So they are buying in more support.” She mainly does consultations at her Harley Street clinic. “I don’t go to people’s houses,” Grace explains. “I prefer to work with parents, giving them the tools and confidence to do it themselves.”

What about the parents who are exhausted but can’t afford a personal sleep adviser? Simpson tells me they run group workshops costing £25 per person, while Grace says: “Many NHS areas have sleep clinics though there might be a waiting list. And there are loads of books and websites where any sleep trainer worth their salt will post free advice.”

At the NHS sleep unit at Evelina London Children’s Hospital, where 4,000 babies and children are seen each year, Professor Paul Gringras tells me he worries about the sleep training industry being completely unregulated. “A lot of the advice given is not magic,” he says. “Anyone can get it from the internet, but it’s about giving parents confidence to follow it through.”

What about the basic (and unprofitable) fact that, whatever you do and however exhausted you become, babies just take time to sleep through the night? “You can get obsessed about this issue,” Gringras admits. “It’s important to say that babies will wake a lot through the night. The chances are it’s going to settle down, so don’t panic.”