McKinnon and his lawyers are concerned that if he is extradited to the US he could face up to 70 years in jail and millions of pounds in fines and are appealing to the UK government on his behalf.
The appeal follows last week's decision from the European Court of Human Rights not to support McKinnon's claims.
Despite the ruling, lawyer Karen Todner has told the Home Office that removing McKinnon from the UK would be a breach of his human rights. The Home Office is said to be considering the claim.
A peaceful demonstration is planned for outside the Home Office today at 4pm to support the appeal.
Todner maintained that the punishment likely to be meted out by the US justice system would be disproportionate to McKinnon's crimes.
"The US are being very heavy handed and are looking to make an example of him," she said.
"Under the UK system he would face three to four years in prison. Over there it could run into decades in a super maximum prison.
"If he is extradited I would expect the UK government to request diplomatic assurance, meaning that he would serve his sentence over here."
Todner added that McKinnon's suffering from Aspergers Syndrome should also be taken into account.
McKinnon, an ex-systems administrator who is also known as 'Solo', is accused of breaking into US government and Nasa computers in 2001 and 2002.
Although he claims not to have caused any damage, he did leave a note on one machine.
That note read: "US foreign policy is akin to government-sponsored terrorism these days ... It was not a mistake that there was a huge security stand-down on September 11 last year... I am SOLO. I will continue to disrupt at the highest levels."
McKinnon is accused of causing damage to systems and rendering them inoperable. He has always claimed that he was looking for evidence of extra terrestrials.
Originally arrested by the UK's NHTCU under the Computer Misuse Act, McKinnon has been something of a judicial hot potato.
It was originally thought that he would face only community service in the UK, but he was later indicted by the US. The extradition process began in 2005.