Police can check your internet history but only with a search warrant of your computer or a search warrant of your internet history to obtain the internet history from your internet provider.
Your internet provider keeps records of your browsing history and download history for around 6 months to a year and although the Internet provider does not really care what you download as long as it's legal they can see it when they need too.
The internet provider is not sitting there looking at everything their customers are downloading or viewing because it does not interest them and they do not have the time or manpower to do so.
But if a court orders them to get your internet history then yes the police can get the internet history so you cannot hide something if you do download something illegal.
As long as you're not downloading illegal things or doing anything illegal on your Internet service then there's nothing to worry about.
The police do not sit there and watch peoples internet history either as they don't have the time to do so and they can't do that anyway.