Problem we have is that GSV latest view doesn't show the signs, but if you turned in off New Heston Road, you would have come across the restriction signs face-on, so difficult to refute that you didn't see them. If you are prepared to do some legwork and show us what a motorist sees as they drive south down Westbrook Road, it would help.
There may be a 'technical' appeal based on council failure to follow the regulations, but nobody has suggested anything so far. What you could do is go onto the Hounslow website and its pages for submtting reps against your PCN. You should see the list of statutory grounds for reps; anything else is unlawful.