A quick google (not knowing much about this) suggests that transporting frozen embryos cross border is entirely possible (with the right permits):
http://forums.fertilitycommunity.com/fo ... -a-new-lab
So you'll have to prove why it's not viable to transport in order for that argument to succeed.
I think you're going to have a REALLY hard time finding any case law or any references for this kind of circumstances. The number of immigrants who will have frozen sperm in the UK is low ... the number of those immigrants who want to apply for leave to remain on that basis alone will be even lower.
This article suggests there's 100,000 to 200,000 frozen embryos in the UK.
http://www.telegraph.co.uk/health/79480 ... abies.html Let's assume there's an average of 3 embryos per couple ... that means there are (at best) 66,000 couples going through this process.
The 'foreign born' population of the UK is running at around 12% (
http://en.wikipedia.org/wiki/Foreign-bo ... ed_Kingdom) - so let's say (at best) that number is therefore 8000 foreign born couples with embryos frozen. So now we have to divide that up into people with no leave, temporary leave, permanent leave and british citizenship (as that's 'foreign born' - not 'still immigrant').
I can see how the number of people with no leave, from India (which is important given the cultural issues) and frozen sperm/embryos is going to be in the tens, if not single digits.
You're going to need a really good solicitor on this.
*Edit: I realised I'm conflating frozen embryos and frozen sperm here across my examples - but I'm just using the numbers on embryos as they are easier to find!