Backpacking

I am planning on taking a short backpacking trip through the UK (two weeks) this November. I expect the weather to be cold and for a fair amount of rain. However, I hear that many historical attractions are either closed or reduce the amount of hours they are open during the winter season. I’ve also heard that its much cheaper given that it is off-season and I am on a budget. To me this outweighs the limited hours. But I was wondering can I still have a fairly decent time considering the weather and the limited hours of operation?