“Muslim women must learn English or risk deportation”.

That was a typical headline today after the Prime Minister announced a £20m fund for English lessons for “isolated” women and a new language test for some immigrants.

Mr Cameron said there were 190,000 women in the UK with little or no English. The government wants Muslim brides who apply for permission to stay with their husbands in Britain to face tougher language tests.

In an interview with the BBC’s Today programme, he appeared to suggest that even women who have children after coming to the UK might be forced to leave if they don’t improve their English.

Do Muslim women struggle with English?

The PM said 190,000 Muslim women – 22 per cent of the population – had little or no English.

This number comes from the Office for National Statistics and can be found by clicking on the fifth table in this list.

The figures – based on the 2011 census – show that nearly 152,000 English Muslim women and girls aged 16 and over “cannot speak English well” and another 38,000 “cannot speak English”. That is indeed about 22 per cent of Muslim female over-16s recorded in the census.

The percentage for women who gave their religion as Hindu was just under 13 per cent, although that may not be a useful comparison – the average Hindu woman might have been living here for longer, be better educated, or have started out with more English.

We would really want to know how Muslim women’s English skills compare to women with similar backgrounds and profiles who follow different religions, but we don’t have a control group to hand.

We don’t know from these figures how many Muslim women with poor English are recent arrivals, or how likely Muslim women are to improve their language skills over time compared to other groups.

The figures don’t prove or disprove Mr Cameron’s claim that many Muslim woman speak “little or no English despite many having lived here for decades”.

Is there a link between language proficiency and extremism?

David Cameron has been mentioning these issues in the same breath since at least 2011, when he said “making sure immigrants speak the language of their new home” should be part of efforts to tackle radicalisation and Islamic extremism, and it’s possible to trace the idea back to the last Labour government.

But to our knowledge, ministers have never put forward an evidence base that shows how failing to learn English leads to radicalisation.

As pointed out today, some children of immigrants with imperfect English – like Conservative peer Baroness Warsi – have achieved high office.

PS mums English isn’t great yet she inspired her girls to become a Lawyer, teacher, accountant, pharmacist, cabinet minister #WomenPower

— Sayeeda Warsi (@SayeedaWarsi) January 18, 2016

And we know from recent police appeals that some parents of radicalised young Muslims who have travelled to join the so-called Islamic State in Syria speak impeccable English.

In fairness, Mr Cameron did specifically rule out the idea that poor language skills breed extremism in his Today interview, although he made a link between the two things in the very next sentence:

“I’m not saying there’s some sort of causal connection between not speaking English and becoming an extremist – of course not, that would be a ridiculous thing to say.

“But if you’re not able to speak English, you’re not able to integrate, you may find, therefore, that you have challenges understanding what your identity is and you could be more susceptible to the extremist message.”

What is the new language test?

The government has said it will introduce another English test, not just for Muslim women but for all non-EU immigrants who come to Britain to join their husband or wife.

Immigration rules are fiendishly complicated and there are lots of exceptions for different groups, but most people who aim to live in Britain after marrying someone settled here are already required to sit language tests.

To get a “spouse visa”, the rules state that you must prove you have an “A1” (very basic) level of English. If you want to apply for indefinite leave to remain five years later, there is another test to make sure you have achieved B1 or intermediate English.

Today’s announcement basically introduces an intermediate stage. After two and a half years people will be expected to have achieved A2 level, mid-way between A1 and B1.

Will Muslim women be “deported” if they fail?

It’s hard to know how tough the government really intends to get over this new test.

In his BBC interview, Mr Cameron appeared to suggest that even women with children born in this country would not be guaranteed a future here if their English was substandard.

But immigration lawyers are questioning whether this would work in practice.

Stephanie Harrison QC from Garden Court Chambers, an expert in immigration and human rights law, said failing a language test is not currently  a basis  for removal from the UK.

“There are language requirements, but if it is a genuine relationship – a genuine marriage – then it is not going to be a sufficient  legal basis (for removal). That is not what the position is at the moment.”

The government could change the rules to make language proficiency a mandatory  requirement, but they  would undoubtedly find the policy challenged by lawyers as a potential breach of Article 8 of the Human Rights Act and of the Equality Act 2010, she said.

Article 8 protects the right to private and family life, and lawyers would argue that removing, say, the mother of children born in the UK, was a disproportionately harsh penalty for failing to pass an English test.

Ms Harrison QC told us: “The government would also have to demonstrate that they had had regard to the best interests of the child under section 55 of the Borders and Citizens Act 2009 and I could envisage no basis upon which a court would conclude that it was in the best interest of a child to remove their mother because she had not reached a certain proficiency in the English language.

“Removal or even the threat of removal of a parent would be damaging to the rights and welfare of a child  and disproportionate.”

The government could also be challenged under section 149 of the Equality Act, she said, adding: “It just simply could not be sustained on a whole number of levels.

There is no relationship of proportionality between a person’s ability to have a certain level of English and their family or private life in the United Kingdom. It is a nonsense.”