For primary schools it must vary from school to school since we see stories on here from parents whose children are having to learn them. But many mustn't be doing it well because so many arrive at primary school unable to work out even simple ones like 4x6 or, even worse, 6 x 10. And even if they know 6 x 5 =30 too many would have no idea what you mean when you ask 'so what's 30 divided by 6. Hopefully jourdain's child will benefit from having to know the reverse times tables.
Secondary school is more difficult. 8 year olds may be happy and compliant when chanting times tables but getting 12 year olds to do it is a different matter.
Mental arithmetic is also not as good as it should be. Pupils too often just don't have mental strategies to do simple calculations such as 40 - 19.
I would like there to be some sort of mental arithmetic test students have to pass at certain stages but I know some teachers disagree. The problem is that the GCSE covers just far too many things and the GCSE results- getting a grade C (4/5 now) is so important. So even the students who can't do 6 + 7 by age 16 without a calculator have to be taught how to calculate the volume of a triangular prism, manipulate surds or simplify (y+4)(y-6).
I think we need to accept that students are not suited to GCSE Maths and we should have some sort of mental arithemetic qualification, and lessons should focus on that.
Of course some students are just not interested in learning and don't see the point, so you can't force them to improve.
I think parents have a part to play in this too. I leant my mental arithmetic playing counting games or by just being quizzed. My children did the same. I knew my tables before I was six. It's not hard- if children can learn a language (English etc) at home by the age of 5 learning some times tables and number bonds shouldn't be a problem.