Do 22% of Muslim women in the UK speak little or no English?
No but census data is somewhat consistent with the notion that around 22% of Muslim women, born outside the UK, report themselves, or are reported, to the census as "cannot speak English well".
The census figures relate, not to Muslim women as such but to UK women born in Pakistan and Bangladesh. The Muslim Council of Britain seems to consider that the latter is representative of the former.
David Cameron
British Prime Minister David Cameron posted on Facebook
Consider this: new figures show that some 190,000 British Muslim women – or 22 per cent – speak little or no English despite many having lived here for decades. 40,000 of these women speak no English at all. So it’s no surprise that sixty per cent of women of a Pakistani or Bangladeshi heritage are economically inactive.
Politicians of all hues often make simplified statements about complex matters and choose numbers that suit their political agendas. The numbers may be real but, by themselves, may not give a complete, balanced or accurate view of the subject.
There are figures, from the UK Census 2011 that seem supportive of the government's assertion.
Other figures seem to contradict the assertion.
It may depend on exactly how you define "little or no English", "Muslim" and "struggling with English". For example does struggling mean only those actively seeking to learn in a formal organised setting and experiencing some difficulty?
It also depends on how representative of UK Muslims are immigrants to the UK from Pakistan and Bangladesh.
Muslim Council of Britain
The Muslim Council of Britain (MCB) published a report that contains the following

Note that the MCB advance the idea that these national groups may be an indicator for muslims in the UK. The figures for "cannot speak English well" are 18.8% and 24.7%. It seems conceivable that the government's figure of 22% may be some kind of weighted average of these or of similar or overlapping data.
The MCB also published an Infographic that contains this

We don't know if the 6% includes or excludes Muslims who speak no English and make no attempt to learn English - The census figures don't tell us if if there are any UK Muslims at all who are content not to speak English and are therefore not "struggling".
In the, perhaps unlikely, event that the 6% are all women, not men and are all foreign-born, not UK-born; the 6% would then be 24% of foreign-born Muslim women in the UK.
Some notes:
- The above data doesn't distinguish between men and women.
- The 6% seems to be for British muslims.
- The other numbers exclude British-born muslims.
- Other figures in the report and infographic are for England & Wales only.
Serena Hussain
A book "Muslims on the Map: A National Survey of Social Trends in Britain"
By Serena Hussain in 2008 gives the following on page 121:
Muslim women were least likely to report English as a spoken language, when compared with women from other faith groups. 73 per cent of Muslim women could speak English compared with 76 per cent of Buddhist, 81 per cent of Sikh and 90 per cent of Hindu women.
This seems to have been drawn from sources including the 2001 census.