I think it will work this way. The UK has birth certificates and will issue them 'backdated' so there is no problem. The reason it is difficult trying it the other way here is that the family book thing gets in the way. The Swiss have one of those things. It is a bit like the French way of doing it. So what we found was that by getting the bit of paper in the hospital that shows the child is yours and trotting off to the Swiss Embassy in London we got the family book and a month later a passport on the way. Off we went to the registry office a bit later, showed them the Swiss family book and got the UK birth certificate. Nobody raised any questions.
With our first daughter we had registered her normally as UK, which meant the bit of paper from the hospital was gone. When we went to the Swiss Embassy in London the last thing they want to see was a UK birth certificate but wanted the pro forma or family book rather than a UK birth certificate. So they messed us about a bit. That way when the second was born we went for reverse order and it worked.
So Nick, my rationale is that when you go for the belated UK registration they will take whatever you have to show where, when and so on, as long as they are clearly your progeny, have a dekko at your passport or birth certificate if it is available and will get you to sign the appropriate forms, extort a vast amount of money out of you for each one and you will soon have them.