Is international iMessage free?

Your friend may get charged if they were sending iMessages using a cellular connection, especially as they would have been "roaming" at the time. That would be a charge levied by the carrier and the UK mobile network that they were logged onto at the time. If your friend was using a wi-fi connection however, then there would have been no charge.

There is no charge from Apple to use iMessage.

You may pay data charges depending on your carrier.

You might also want to make sure that "Send as SMS" is turned off for now, so that if the iMessage fails, you are not charged for an international SMS.

Yes. You can send an iMessage to anyone anywhere in the world for free.

Hope this helps