Last bit first:
Since there's no statutory definition of a 'garden flat' it's unlikely that any law has been broken by advertising it as such. (The definitions used by estate agents are notoriously flexible with, for example, properties frequently being offered as being in a neighbouring borough; it's up to prospective buyers to check out the realities behind estate agents' statements).
Next:
Have you actually seen what's on your neighbour's title documents (rather than just taking his word for it)? Download the title register and plan, for £3 each, from here in order to check:
https://www.gov.uk/search-property-information-land-registry
The definition of "on foot" though encompasses both the pushing of a perambulator and the wheeling of a bicycle:
http://www.boundary-problems.co.uk/boundary-problems/priv-r-o-w.html
so it might be hard to argue against pushing a motorcycle as well.