It's not unreasonable, but if after taxing 3rd and 4th homes (etc.) to oblivion the issue persists, then also second homes should be taxed high. I truly believe that extreme would not be needed once it's made humanely forbidden to own multiple homes without intention of ever living in them.
Worth adding that it should not be the number of homes what should be taxed, but based on the market value of those properties.
Good. However, if the intent is to discourage driving in central London, the penalty should not be an fixed rate for each vehicle. It should be a dynamic rate based on how much the people in the car earn. Otherwise you are only displacing people with low salary while freeing the roads for the rich that don't care to pay £30.