Jac, i'm guessing in a pedantic world then yes it is illegal.
However in real life... you would have to find the most pedantic, stressed, hungry fat policeman in the world to try and actually do you for it.
I've been pulled a hundred and one times, i've found if you're sound with the police and talk to them with a little respect then they're alright with you..
Apart from one or two stereotyping power hungry stuck up bell end coppers that are out to save the world from us highly dangerous criminals driving around with no backseats.
Disclaimer, i'm not a solicitor and neither are (from what i know of) the members of saxperience, we dont know the law inside and out, if you want to know the correct answers to any legal questions you're best off asking at your local police station.
Could you not get the dog in the back with the seats just folded down as normal without the bottom half removed? They only tilt like 20 degrees. Or how about taking the bottom half out, folding the back seat down, then put the bottom half in the boot for the dog to sit on?
Just food for thought, my neighbour has a people carrier, with removable seats. His wife is disabled and they carry the wheel chair in the back. To do this he removes his removable seats... Does he have to phone his insurance company everytime he takes a seat or two out or put them back in?

Just something to ponder on.