At the time a Palestinian with some British rights. If you left prior to May 14, 1948, I suspect that you wouldn’t have qualified for Israeli citizenship. Unless you immigrated to the United Kingdom by a certain date, you would have lost a claim for British nationality but quite qualify for a British passport saying you are a British national without right of residence in the UK.If you moved to the US pre-1948, but neglected to pick up American citizenship, and it turned out weren’t eligible (say, if you are a felon), it would be an interesting question whether the Israelis would let you in when the US deported you as an illegal undesirable alien.