It seems strange to me that my daughter – white and very obvious British in many ways – can read,write and speak Bangla better than most of my Bangladeshi origin British friends. I don’t know if this is common in Europe or if it is just the curse of the British ‘Island mentality’.

Mike, my need is not “urgent” and my goal is not that my children speak the family language to perfection. This was never my goal. I changed the text a bit where I think my message was not clear enough and lead you to assume I have higher expectations for my children.
Anyways, we all have certain expectations when it comes to our family languages. Usually we want our children to be able to speak the family language(s) and maybe be able read and write in that language(s). If you acquire or learn a language while living abroad, most probably you will not attain the same level of fluency (oral and written) as a child who is exposed to the same language in a monolingual setting. This becomes even more visible in children whose parents already grew up abroad and don’t have such high expectations for one language: they tendentially put more effort in their children to become multilinguals!
My experience in my praxice is that many parents – mainly those who grew up in their home country and now raise there first generation of international children – have quite high linguistic expectations for their children. Sometimes these expectations are very unrealistic: a child that grows up abroad can not use the language in as many contexts as someone who grows in a monolingual context.
I don’t feel bad that my children are not as fluent as peers in Germany, Austria or Switzerland. My children are multi-lingual and multi-cultural, like myself and I consider this as a great asset. And, yes, we live our own authentic reality, like you say.