With her daughter stillborn and her husband suffering from depression, Jessica Nicholl and her MP Vince Cable are fighting her deportation back to the US

A couple grieving for their stillborn daughter face being split up, after immigration authorities ruled that there was insufficient justification for them to be allowed to stay together in Britain.

Despite the intervention of the couple's local MP, the business secretary, Vince Cable, a judge last week refused Californian Jessica Nicholl's appeal to stay with her husband, John, who is suffering from depression.

She has been told to return to the US by Thursday, after which she will have to go through the process of applying for a spousal visa before the couple can be reunited.

John, who had a string of family bereavements – including the deaths of James, his baby son from a previous relationship, and that of his father – before he met Jessica, has been in an especially fragile state since the death at birth of the couple's daughter, Meadow.

"I am really concerned about his wellbeing, we have both been relying very much on each other to get through this and I cannot bear to think what will happen if I have to leave him on his own," said Jessica, 23.

The pair met online five years ago and married in August 2009. They set up home in Twickenham, south-west London, to be close to John's children from his previous relationship.

"I came over on a visitor visa and didn't think anything of it," said Jessica. "We hadn't even realised there would be an issue until after we got married and I had fallen pregnant, which is when we started to look into immigration and visas in depth and realised just how complex and difficult it really is."

Cable has written to Damian Green, the immigration minister, calling it a "deeply tragic case". Describing Jessica's predicament, the letter states: "Her attempt to regularise her status as a spouse has been unsuccessful. Clearly things have not been done as they would have been in an ideal situation. Nonetheless, we are where we are and this is a couple who are devoted to one another and dependent on each other's support following the loss of their baby and the process of mourning and bereavement."

The couple are appalled by the legal nightmare in which they have found themselves. "It's still a shock to us to be presented with the situation where a husband and wife aren't allowed to live together," said Jessica, "or even stay and support each other through such stressful and traumatic experiences as losing a child.

"We need time to get over this, together. They are most likely going to let me back in, so why do I have to leave him at all?"

She was also "deeply hurt" when Meadow's death was described as a miscarriage when her appeal to stay was being considered. "I found it very offensive. That was our daughter and the judge dismissed our grief in a sentence."

West London Sands, a self-help bereavement charity for those who have suffered a neonatal or stillbirth, said it was common for such losses not to be considered on the same level as the loss of an older child. Colette Murphy, from the charity, said: "Jess had a really bad time when Meadow was born, a particularly traumatic birth. Unfortunately, time after time we see the loss of a baby undervalued."

There is no available parental home for Jessica to go back and live in while her spousal visa application is processed. "Our family in the UK is guaranteeing to support me if necessary," said Jessica. "I am willing and eager to work, pay taxes and contribute to the welfare of my new home, as well as giving up any rights to any social benefits. I want to work in the care sector. It seems unfair to punish John for his condition, especially because of the lack of control he had over the circumstances that triggered his condition."

The couple's lawyer, Duncan Grant, said: "What right-minded person would say they have to be split up now, when they clearly need to be supporting each other? They are quite clearly in love and reliant on each other."