"Anthony Eden sent the Yugoslav regent a message asking him to join the Allies. They also told the Yugoslavs that defending Salonika depended on what Yugoslavia did. The British were so committed to going into Greece that they had no choice but to proceed." The large troop convoys that were at sea pretty much forced their hand.
The British were planning on trying to defend the "Vermion-Olympus" line. The accepted that they might be forced to withdraw, and saw that there was a good possibility of successfully "staging a fighting withdrawal." 7 March was when British cruisers had disembarked several thousand troops "at the Pireaus".
You might well ask "what had been done to inform the Australian and New Zealand governments? In February, the British had met with Mr. Menzies who hd been Prime Minister at the time. Already, there was concern about a Japanese threat in the Far East, although that only turned into an attack in December. This was a time of political turmoil in Australia, where they changed governments multiple times in a short period of time.
The New Zealand government, lacking much information, had agreed in principle to the Greek campaign. They wanted to see the 2nd New Zealand Division "fully equipped with an armored brigade". New Zealand was happy to take part along with the Australians. The new Australian government was only "conditionally agreed to participate". They wanted to know that there was a plan in place to evacuate if the situation turned out badly. This is based on the account in "Greece Crete and Syria" by Gavin Long.