You are mixing quote validity( that is how long a quote to start on a certain date is valid) and difference in premiums for policies that start on different dates. Your aggregator quote above for a policy to start next week isn’t valid for 28 days, after that proposed date a new one is required which may well give a different premium and if the start date is closer to today than the original it will most likely be higher.
Moral of the story, know when your renewal/purchase date is due, get the quotes as long as you can in advance and accept it close to the time to keep the money in your bank but don’t change the start date unless it’s unavoidable.