If the grassed area is a communal area then you can’t run a cable over it, it has to be buried to prevent tripping (whether anyone will walk on the grass or not). In my case I had the KerboCharge cable gully fitted into the footpath by my local council at a cost of £300.
I also don’t have a designated parking space, all I had to do was say I accepted that someone else may park where I usually park (small cul-de-sac and never happened in about 11 years) and that if they did I wouldn’t be able to charge, and wouldn’t then run the cable over the path or the roadway instead.
Please excuse spelling/typos. Apart from being a clot it turns out I had one on my cerebellum that's now causing various problems!