Another study, meanwhile, ranks three fertility doctors at the hospital of the Free University of Brussels (VUB) among the top 10 in the world.
"Until now, we have only had anecdotal evidence of this phenomenon," says Françoise Shenfield of University College, London (UCL), who coordinated one of the studies. The information was presented to the annual congress of the European Society of Human Reproduction and Embryology in Amsterdam at the end of June.
The UCL looked at six countries considered to be among the most popular destinations for fertility migrants: Spain, the Czech Republic, Belgium, Denmark, Slovenia and Switzerland. Those six countries alone take in about 10,000 patients coming from abroad every year. (The calculation is made according to the number of fertility cycles concerned - between 20,000 and 25,000 - although one woman may be responsible for several cycles).
Four countries, meanwhile, supply the majority of patients: Italy sends by far the greatest number, with nearly 32% of the total, followed by Germany, the Netherlands and France. The rest are patients from no fewer than 45 other countries.
The main reason given for travelling abroad for fertility treatments is the severity of regulations in the patient's homeland. Those vary from country to country, but new regulations introduced in Italy in 2004 led to a major increase in fertility migration.
The inability of lesbian couples in France to get access to in vitro fertilisation - French law restricts treatment to heterosexual couples - makes them one of the main groups of fertility migrants to Belgium. British patients travel abroad because of the change in the rules on anonymity in cases of donor sperm and eggs. However, the UK patients interviewed were the main ones to cite a second reason for fertility migration: the difficulty of access to treatment at home.
Geographical and language issues play a role in which destinations are chosen. Italians tend to travel to Spain and Switzerland; Germans go to the Czech Republic. The French prefer Belgium, and they are the largest single group to travel here, accounting for 38% of cases in the years 2005-2007, according to figures from the Bioethics Institute Ghent.
Next come the Dutch, who are attracted not only by the language but also by the more relaxed age limits: in the Netherlands, clinics will only treat women up to the age of 41. In Belgium, treatment can start right up to the 45th birthday, and clinics will implant previously-stored egg cells in women up to the age of 47. In the study, 51% of the German migrants and 63.5% of the British were over 40. The average age was 37.5 years.
"Apart from that, the reputation of our centres is very good," says Guido Pennings, a bio-ethicist at Ghent University, who advises the Centre for Reproductive Medicine (CRG) at the VUB University Hospital and headed up the Ghent study.
Dr Pennings' study looked more closely at the situation in Belgium. He discovered that some patients come here only after failed attempts at pregnancy in their own countries. "If patients have had a couple of attempts in their own country without success, they may want to make a final attempt in a centre abroad that has a good name," he explains.
Cost is an important factor: only 3.8% of cases looked forward to being fully reimbursed by their medical insurance for treatment abroad, with about 13% receiving partial reimbursement. The other 83% were paying out of their own pockets.
The CRG, housed at the main university campus in Jette, is widely considered to be one of the best in the world, with researchers under Professor Paul Devroey responsible for a number of important developments in the field. (Full disclosure: this reporter's own two children, now aged 15 and 11, were the result of treatments by Dr Devroey's team.)
The CRG website has special instructions for people coming from abroad for fertility treatments, including advice on how to organise blood tests and ultrasound scans in your own country and communicating the results to the CRG. "There are no hard and fast rules," the website advises. "Our only aim is that the treatment proceeds as effectively and comfortably as possible."
Some couples coming from other European countries and farther afield rent mobile homes and stay in the hospital car park to save on hotel bills while going through the lengthy and arduous procedure. The procedure itself is also expensive: one in vitro treatment starts at €4,900, excluding drugs, the initial consultation and screening, and any extra procedures required (including the dauntingly-named "electro-ejaculation", which costs €1,300 with anaesthesia, or €500 without).
"We get a lot of patients for in vitro and such treatments from the Gulf States and from Scandinavia," explains Professor Herman Tournaye, head of department at the CRG. "That's mainly because of our name."
In a recent survey by Fertility and Sterility, the main journal of the American Society for Reproductive Medicine, Dr Tournaye ranked seventh in the world for scientific influence in the area of fertility. At the top of the list is Dr André Van Steirteghem, the retired former head at the CRG, just ahead of Dr Devroey.