To start with, participants were told both they and their partners would secure financial rewards for accurate estimates.
The scenarios were then repeatedly changed so that, in some cases, participants benefited if they deliberately over-estimated the number of pennies.
When told that lying about the amount would benefit them but disadvantage their partners, volunteers initially exaggerated only slightly. This prompted a strong amygdala response, revealed in brain scans.
But over several runs using the same scenario, the exaggerations became more and more pronounced while amygdala responses declined.
Larger drops in amygdala activity predicted bigger future lies, the study found.
Dr Tali Sharot, an experimental psychologist at UCL said: "When we lie for personal gain, our amygdala produces a negative feeling that limits the extent to which we are prepared to lie.
"However, this response fades as we continue to lie, and the more it falls the bigger our lies become. This may lead to a 'slippery slope' where small acts of dishonesty escalate into more significant lies."
Dr Neil Garrett, the lead author who is also from UCL, said it was likely that the findings reflected a blunted emotional response to lying.
He added: "This is in line with suggestions that our amygdala signals aversion to acts that we consider wrong or immoral. We only tested dishonesty in this experiment, but the same principle may also apply to escalations in other actions such as risk taking or violent behaviour."
The amygdala consists of two almond-shaped nerve bundles embedded deep in the brain which are linked to fear, anxiety and social phobias. They also play a role in controlling aggression.
Studies have shown that many psychopaths, who lack empathy and are often accomplished liars, have unusually small amygdalas.
The new research is reported in the journal Nature Neuroscience.
Dr Raliza Stoyanova, a member of the neuroscience and mental health team at the Wellcome Trust charity, which co-funded the research, said: "This is a very interesting first look at the brain's response to repeated and increasing acts of dishonesty.
"Future work would be needed to tease out more precisely whether these acts of dishonesty are indeed linked to a blunted emotional response, and whether escalations in other types of behaviour would have the same effect."