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thats what happens when you allow mass uncontrolled migration - we should be careful here.
As you've drawn the comparison between Israel and UK - the mass immigration to Israel are Jews from around the world.
Thus the similar scenario for UK would be all ex-pats around the world, and their offspring for the last thousands of years, irrespective of where they were born, but because they have a tenuous link to one great great grand parent who may have been English, (but records didn't exist then), being allowed to migrate to UK.
And there is so many of them that the UK invades Ireland, dispossesses all the Irish, kills them if necessary, and drives any survivors out of Ireland to create English settlements.
There would be a problem of course, because all those with English ancestry, in USA, Australia, New Zealand, South Africa, the Caribbean, South America, Canada, etc would all have a right to come and settle in the UK, as long as they could claim some tenuous family connection to a British person way back in the doomsday book. I doubt if just Ireland would suffice, so UK would have to go on a great expansion, through violence, to colonise additional land. Any "white British" migrants would be allowed, in addition, to retain their 'other' passport, property, possessions, financial links to their 'adopted country.
Do you understand how inherently and aggressively racist that policy would be?
But it is the policy of Israel.