Presumably, there is a reason why you are going in November. Yes you can drive from London to the Lake District in under a day. Just don't plan on it only taking 5 hours to a specific point. Drive times are longer than you are used to at home, simply because of volume of traffic and roads that you really just can't drive as fast for long periods of time before coming to something that slows you down.
At least no one will be trying to tell you that you absolutely need to book hotels ahead in November and that includes Skye. LOL