LAKE SUCCESS, N. Y., March 28--A British spokesman said late today that the Palestine problem probably would be turned over to the United Nations within 24 hours along with a request for a special session of the General Assembly to start work on it.

This development can as it was learned the United States had sent a note to the British Foreign Office declaring this country had no objections to a special session on Palestine.

The spokesman said British delegate Sir Alexander Cadogan was prepared to act as soon as he received a go-ahead from London. He said such instructions could be expected immediately unless the United States note contained some qualifications which early reports had not mentioned.

United Nations officials indicated they would canvass the 55 member nations as soon as the British request was received. Approval by a 28-nation majority is necessary before a special session can be called.

The only major opposition was expected to come from the five Arab states in the U. N. Faris EI Khoury, Syrian delegate to the Security Council and leading Arab spokesman here, said the Arab countries would vote against a special session unless the British request was accompanied by a recommendation for a solution of the Palestine problem