The Luton planning guidance is nearly ten years out of date!
Newer planning guidance that permits cramming of homes on sites and increasing density all but did away with parking space and driveway requirements. If Luton are hanging on to theirs good for them, but they would lose on appeal if they refuse planning on any of these grounds.
If you look at Appendix 3 2(e) it states that the internal width of a garage (with walls!) should be at least 2.2m yet a space without walls (or fences) needs to be 2.4m wide.
Like you, I am surprised the NHBC standards do not have a minimum size requirement for garage, drive and parking space drives widths.
You will only have a case using the Consumer Code if the parking space is less than 2.4m wide or less than stated on plans. Be sure to claim your £120 fee and the £250 maximum for "inconvenience."
Not sure what remedy you have unless you go for loss of property value which is excluded under the Code adjudication. Read the
Consumer Code for Home Builders pages on my website for more information.