My understanding is that late term abortions in Canada take place in hospitals not clinics and the data is separated by location.
There are certainly problems with access in Canada, as there are everywhere, but the law (or lack of law) in itself does not appear to be a problem. I don't believe it would be a problem in the UK and I think it would solve the two problems I posted above.
The article you linked to argues that because there is no law, there is no legal right to an abortion. This is technically true, however:
'the right to an abortion doesn't exist in Canada in the same way it is enshrined in Roe v. Wade.'
We saw how that worked out.
Another way of looking at it is this: If there is no law, then there is nothing that can be chipped away at. We wouldn't have private members' bills seeking to lower the time limit every few years.
When R v W was repealed, WHO made a strong statement that abortion is healthcare. We should start treating it as healthcare instead of as a matter for criminal law.
That doesn't mean a woman with a healthy 39 week pregnancy could demand an abortion and the doctor would just say 'ok then', any more than they would agree to cut off her leg, just because she asked. Doctors are duty bound to act in the best interests of their patients (for the avoidance of doubt, the patient is the pregnant woman). It simply means that doctors would be able to act in the best interests of their patients, at whatever stage of pregnancy, without the additional constraints of strict time limits and fear of prosecution.