Newcastle University has already produced a human-animal embryo
Campaigners are seeking permission to launch a High Court test case over the regulation of controversial research.
The Christian Legal Centre and Comment on Reproductive Ethics have claimed the Human Fertilisation and Embryology Authority (HFEA) operates unfairly.
To demonstrate their point, they will cite the way human-animal embryo research was given the go-ahead.
But the regulator said all decisions were made in a transparent way that followed correct procedures.
The two campaigners want the case to be heard under "public interest" rules whereby costs are capped.
A High Court judge will hear the arguments on Wednesday, but is not expected to make a decision for several weeks.
They are challenging an HFEA ruling earlier this year to grant licences to scientists at Newcastle University and King's College London in January. A third team in Warwick has subsequently been granted a licence as well.
Supporters of inter-species research say their work could one day help to treat serious diseases.
But Josephine Quintavalle, spokeswoman for Core and a named party in the action, said the regulator was "too pro-embryo research" and did not give opponents enough of a voice in the decision-making process.
"The way the regulator works is not fair. No-one representing the interests of the embryo can sit on the committees that make decisions and once a decision has been reached we cannot appeal it."
She also said the HFEA acted outside its jurisdiction - at the time of January verdict a bill was still in the process of being drawn up covering this very issue.
That bill has now been passed and will come into force next year allowing such applications to be considered.
The HFEA has always maintained it was right to consider the original application as the 1990 law it was working under stipulated the regulator was able to interpret guidance as science progressed so as not to slow down research.
A spokeswoman also denied suggestions its decision-making process was undemocratic.
She said each new application was subject to a public consultation, expert review and HFEA committee hearing - members of which were appointed by an independent body.
"It is a fair and transparent process."