An Australian family is facing imminent deportation was still hopeful last night of remaining in the UK despite apparently missing a deadline to meet visa requirements

Kathryn and Gregg Brain, who live in the Scottish Highlands, had until midnight to secure a job for Mrs Brain that meets Home Office visa requirements, after being granted an extension on their leave to remain. But there was no announcement as the deadline passed.

The couple moved from Australia to Dingwall with their son Lachlan on her student visa in 2011, but a two-year post-study visa scheme then on offer was later withdrawn by the Government.

Kathryn and Gregg Brain have strongly criticised the "injustice" of the Home Office's threat to remove them in August after retroactively ending a two-year post-study scheme just three months after they arrived in the Scottish Highlands in 2011.

Their leave to remain in the UK expired at midnight on Monday night. While Theresa May has said "there is a need to follow the rules", a Home Office spokesperson has said any visa application put in by the family up until that time will be considered.

Mr Brain said the family have received around a dozen job offers but none that would meet the specifications for a UK tier two visa. But he said last night they are still hopeful that a 28-day extension can be secured.

Mr Brain said: "As we understand it, you can usually make an application within 28 days of the expiry of your leave period. You lose certain appeal rights because you are late with your application but it can still be done.

"That is the ordinary case. Our circumstances are rather complicated by the extra period of grace that has been given to us and we're still talking to our solicitors just to find out exactly where we stand on that issue, but our understanding is we probably can, if an employer were to turn up, make a late application and that would be considered."

He said they had been operating on the assumption that yesterday was the deadline "but it is a possibility that we may be able to still continue on".

He said they would still be talking to the lawyers today: "We'll be trying to find a way forward and still hoping that the Home Office will see that the honourable course is to do what they said they were going to do when they asked us to come here."

But if the family's "grace period" elapses, the Brains will be expected to voluntarily return home to Australia.

A decade-long dream to move to the UK was thrown into disarray in 2012 when the family, which includes 11-year-old son Lachlan, were first made aware that Ms Brain's visa was no longer considered valid by the Government.

And now a job offer for Ms Brain has fallen through, threatening the deal made by new immigration minister Robert Goodwill that the family could stay on the condition that Ms Brain find permanent work.

Mr Brain said he was disappointed that the Home Office had not upheld "their end of the bargain."

"We spent 10 years trying to plan to get here in the first place - it's been a dream of ours since years before Lachlan was born," he said.

"It's not something we can put aside lightly. It's the injustice of it, the thousands of students who were robbed when this deal was retro-actively torn up.

"I just cannot accept this, I want the UK Government to give us what they promised us when they enticed us to sell our homes and bring that equity to the UK.

"Neither one of us have been allowed to work since mid-March and we have been living on the charity of friends, the church and strangers."

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Despite support from Nicola Sturgeon, the First Minister of Scotland, and rumours that one of Scotland's biggest employers wishes to make Ms and Mr Brain a job offer, a potential post at a local distillery has collapsed as it did not meet the necessary visa specifications.

Mr Brain continued: "At this stage we are still very much hoping that an employer will come forward and we'll be able to continue moving towards a tier two visa application.

"Of course, what I'd really like is for the Home Office to give us what they promised when we moved here in the first place - a two-year visa with the right to work.

"We have fulfilled our end of the bargain and we still very much want the Home Office to fulfil theirs.

"But failing being dealt with honourably by the UK Government, what I would like is for an employer to come forward and take Kathryn on to enable us to get a permit and be able to stay on in Scotland."

Speaking at a press conference, a spokeswoman for Theresa May said: "On that case it is one that ministers have spoken about before.

"I think, in terms of the details, they do have a temporary leave to remain, currently. We recognise the strength of feeling on this case but there is a need to follow the rules, follow the process and to date they have not lodged a visa application with the Home Office.

“They have temporary leave to remain that doesn’t expire until midnight tonight. They have already been given three grace periods of temporary leave in order that they can make an application for a visa."

A day before they were due to be deported on May 31 this year, former immigration minister James Brokenshire gave the family leave to remain in the country until August 1, with his successor Mr Goodwill saying he would be willing to look at extending this if a concrete job offer was made.

Angus Robertson asks about child likely to be deported

Mr Brain added the family had been "stunned" by the response to their plight, with people sending cheques to their local MP to help support them. Other SNP MPs including Angus Robertson and Ian Blackford and MSP Kate Forbes have also called on the Home Office to allow the family to stay.

A Home Office spokesperson confirmed with The Independent that any updates would be given after the deadline on August 2.