4. NB - our code which operates the Used Car Update Facility is copyright, and non-transferable as explained in our original quotation.
Hmm. The client may argue that ownership of the code is not being transferred, and technically it isn't - you developed it for them and they aren't attempting to sub-license it to any other party.
The law generally allows the client (which would include any sub-contractors they choose to work with) a right to repair and upgrade the software in line with the requirements of the company, unless you've explicitly agreed otherwise.
Again, the generalisation is that by taking payment you are granting them a non-exclusive, royalty free and irrevocable license to use your work. If they tried to resell then you'd have a legitimate case, but I can't see how they are doing so.
IANAL, but you might want to consult one if things start getting messy. Unless of course you think pursuing it is more trouble than it's worth, which is unfortunately often the case with things like this
