well, this gets even more interesting. here are some facts;

1. you can not set up a power of attorney in a solicitor's office. It has to be done in Notary Public.

2.Even if we assume that the power of attorney is valid, I understand that you gave it to the lawyer "Y".

3. you did not give any money to "Y"

4. you gave the money to "X" who is not authorized by you (with power of attorney)

The consequences are :

"Y" is not responsible for solving your legal problem because he did not receive any money from you.
"X" got the money but he also has no responsibiltiy because he has not received power of attorney.

If you have a contract signed by "Y" which states that "Y" is responsible for solving your legal problems, and also "y "accepts the payment to be done to "X" then you can claim "Y" to solve the problem. otherwise you can only claim your money back from "X".

If I were you I would hire another independent lawyer to solve this problem otherwise your loss may get bigger.