The government has found permanent homes for about half the Afghans and their families who have been evacuated in the past fortnight, The Times has learnt.

About half the 343 councils in England have offered long-term accommodation under a scheme to protect those who helped the UK mission in Afghanistan. Until yesterday the Home Office could confirm only that a third of councils had offered homes.

It has doubled the number of permanent homes available under the Afghan relocations and assistance policy (Arap), to 4,000. London boroughs account for a quarter.

However, this still leaves more than 4,000 Afghan immigrants already in the UK facing indefinite stays in hotels.

Britain is also still trying to rescue a “desperate” Afghan MP whose dog was hanged by the Taliban after western troops withdrew from Kabul.

About half of Afghanistan’s 69 female MPs have been rescued by western governments. However, Nusrat Ghani, the Conservative MP for Wealden, has been in contact with one who is still there, moving between safe houses, whose dog has been hanged by the Taliban.

“The conversation was very emotional,” Ghani told Stig Abell and Aasmah Mir on Times Radio. “She was in tears, living day by day. I receive messages saying, ‘I’m not sure whether I’m going to survive the night’. This is how desperate she is.”

The Arap scheme is offering local authorities £10,500 for the first year for each Afghan immigrant they can accommodate and support, but ministers are expected to make it a multi-year scheme to ensure that newcomers integrate fully into local communities. Councils are also given £850 per immigrant to pay for English lessons.

An extra £5 million has been put aside as a discretionary fund to help councils house very large families.