By Adam Brimelow
BBC News health correspondent
The British Pregnancy Advisory Service says the lack of abortion services for women who are 20-24 weeks pregnant is a scandal.
The BPAS is responsible for around a quarter of all abortions in Britain
The charity is the UK's largest abortion provider, and carries out 80% of terminations after 20 weeks.
Chief executive Ann Furedi, said doctors and nurses were becoming more reluctant to work in this area.
But she said there were very good reasons why some women left their abortions till late.
Speaking at a conference in London, Ms Furedi said: "It may be that they're very young, and they've been in denial or haven't been able to tell their parents.
"It may be that they've been very ambivalent about the pregnancy and it's taken them a really long time to make up their minds.
"It may be that sometimes they've started off with a wanted pregnancy but something has gone horribly wrong in their lives.
"It may also be that they simply didn't realise they were pregnant because they were using a very reliable method of contraception."
BPAS provides just over 2,000 abortions between 20 and 24 weeks gestation each year.
Ms Furedi called the work "unpleasant and difficult".
She said doctors and nurses are only prepared to do it if they understand the reasons why women present late.
But she criticised what she called ill-informed debate on the issue.
She said it had become current for people to regard early abortion as "easy", so there was no need for late abortion - and that simply wasn't the case.
The current legal limit for most abortions is 24 weeks, although they can be carried out later if there are medical dangers to the mother or child.
BPAS says every year it turns away about 100 women who are beyond the gestational limit.
BPAS has provided information to pregnant women about clinics in Spain and the US that are able to legally perform abortions beyond 24 weeks gestation.
Patrick Cusworth, from the charity LIFE, said it was no surprise that many doctors and nurses do not want to get involved in late abortions.
He said: "Many doctors that we have spoken to have indicated very deep misgivings about carrying out abortions of children that are perfectly healthy, and would have very good chances of surviving outside their mothers wombs if delivered at this particular point.
"The question is, if so many doctors are increasingly unwilling to carry these out, should be tolerating this procedure at all?"