The AC/Mains charger must be able to take alternating current of a wide voltage range and two different frequencies and convert it to direct current of 8.4 V (for an LP-E6). Obviously, you fail to understand the engineering complexities of producing a car charger that must be able to take just a single input voltage that's already direct current and step down the voltage a little bit. For them to charge only
3 times as much for a device that sophisticated, why...it's a real bargain!!
The inverter produces standard Uk voltage and AC frequency + accepts standard UK plugs. So you just plug in your charger as if it were a mains socket. Other than the rather long leads hanging about in the car I cannot see what the problem is. I have tried my Canon LP-E4, CP-2LWE and LC-E4 chargers on in car inverters with zero problems. As I said at the price for the Canon lead (which will ONLY work on my LC-E4) it's a no brainer.
As to Canon chargers being sophisticated?
Only the 1 series chargers allow balancing of the individual cells, and then they take forever to do it! With Lithium cells periodic balancing is important to get the most out of your batteries. The Canon 3 cell charger/balancer Lc-E4 is over 300 GBP in the UK, yet I have far more sophisticated chargers that cost less that 30GBP - pity I cannot work out how to connect them. The Canon/Nikon etc Lithium battery chargers are poor at best and WAY overpriced.
P.S. With my interest in electric powered R/C aircraft I am critical of batteries and chargers