Don't worry about the law change. There is absolutely no need to pay this invoice. It is speculative. Yes the law has changed and if they cannot charge the driver they could invoice the registered keeper.
They cannot issue a penalty charge notice only a parking charge notice.
This is subject to the law of contract. They can only invoice you for their loss which in a free car park is zero! They cannot charge you for costs such as their operatives uniform, office time, tea breaks etc. They have zero chance of success, if you don't believe me then head over to http://www.pepipoo.com/
and check out the forums. They will try to frighten you into paying with various threats
It's your money so your choice but I strongly encourage you to read the pepipoo parking forums. By all means start your own thread over there you will get some good advice.