There isn't much space, can you please move the seat forward?
There isn't much space in the back, can you move the seat forwards?
「せまいので椅子を前に戻してください。」は英語にこのようになります。
There isn't much space, can you please move the seat forward?
There isn't much space in the back, can you move the seat forwards?
「狭い」→ isn't much space
投稿者さんが書いたI'm cramped の英語が近いですが、I'm crampedより It's cramped か It's cramped back here の方がふさわしいです。I don't have much space なども言えば良いです。
ご参考までに。