The line, agreed in conjunction with the US, is aimed at limiting the options of the Israeli government so that it will accept a version of the three-stage peace deal adopted by Hamas.
The UK said its aim was to secure a permanent and sustained ceasefire, and the removal of Hamas from the future governance of Gaza.
The British statement that Israel has presented no credible plan for the invasion of Rafah that complies with international humanitarian law follows a similar statement by the French foreign ministry on Monday.
But Mitchell went further in saying such a move may end up strengthening, not weakening Hamas.
The EU foreign affairs chief, Josep Borrell, said: "The offensive on Rafah has resumed, despite all the demands of the international community, the US, the member states of the EU and all those who have asked Mr Netanyahu [the Israeli prime minister] not to attack.
"Despite warnings and requests, the attack [in Rafah] began at night.
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