嘆願した　って英語でなんて言うの？

Michikoさんの文ですが、pleaded to his people ではなく、pleaded with his people と言うと良いですよ。
あとthe consumption ではなく their consumption と言うともっと自然な感じになります。
ーThe prime minister pleaded with his people to reduce their consumption of tea leaves.

to reduce their consumption of tea leaves の代わりに to cut back on their consumption of tea leaves のようにも言えます。

またはもっとシンプルに次のような言い方もできます。
ーThe prime minister begged his people to not drink as much tea.
「首相は国民にあまりお茶を飲まないよう嘆願した」

ご参考まで！