What are the implications for the UK now that it has these kind of migrants on it's sovereign soil ?.
Not a lot. Firstly, see my post #2 above, they get handed over to the Cypriot government.
Someone elsewhere queried whether, now Cyprus is in the EU, the Dublin agreement takes precedence and the UK counts as the first country of entry.
The answer is, no, the
SBAs are only UK sovereign territory for specific purposes -
and were not incorporated into the EU when Cyprus joined. refugees landing there are no more in EU territory than if they had landed on Ascension Island (And why St Helenans don't get UK residence).
Hence, they would only enter the EU when the crossed the SBA boundary - and Cyprus would be their country of entry.