You're asking two different questions there.
Do you want to fix the price per unit - depends what it is compared with the variable. Either way, you're going to be paying a lot more per unit come January, but which is best depends on what you've been offered.
Should you also try to mitigate the impact of the price rises, by using less? This should certainly be a consideration for some people.
If you have the heating on at night and/or are able to sit around in a t-shirt in winter you can almost certainly use the heating less.
If you wash clothes that aren't dirty, use the tumble dryer when you could line/air dry or change the towels after one use, could you cut down on the amount of laundry you use?
If you cook a lot of things in the oven, could you switch to a slow cooker, air fryer or pressure cooker instead?
If anyone in the household has a gaming PC, that's running for hours and hours, can it be turned off when not in use, and used less?
Remember that one of the reasons why the price of gas is so high right now is that it is expected to be in short supply over winter, which means that we should try to use less so what we have lasts longer, including that which is used for electricity generation.