How do fixed rates work?

Noodler

With a fixed rate energy tarriff you are buying a product at a fixed unit price for a period of time.  When the time period is over, past transactions have no relevance to any future arrangements.  Is a fixed rate mortgage similar, considering it's a loan rather than a purchase?

If I have a 25 year mortgage and for the first 10 years I have a fixed interest rate of 5%, but just after starting the fixed rate the basic rate jumped to 15%, I would be making considerable savings over the first 10 years, whilst the lender would be making a loss.  After the 10 years, how is the remaining amount of debt calculated?  Is the lenders loss written off, added to the remaining mortgage or something else? Thanks.

Gonna-be-debt-free

Yes, fixed rate mortgage is similar to fixed rate energy tariff.

At the end of the fix period you usually move onto SVR, with no holdover to whatever happened with the SVR during your fix period.

The mortgage provider will have done a lot of scenario planning and calculations prior to offering the fixed rate, so that it's their best bet at something they will make money on. If they are wrong then it is them that lose out, not you. 

Conversely, if you decide not to go for a fixed rate, you are doing the same thing the other way around, betting that the rates will stay low for longer. 

Brodiebobs

At the end of 10 years unless you obtained another fix you could go onto the variable rate which is usually BOE rate plus X%.
The lender would just calculate your payments based on the outstanding balance at that point plus the interest rate at that point.
There is no loss to the lender. 

Thrugelmir

In simple terms the supplier of the service/funding locks into a contract themselves to source the item at a fixed cost over a fixed duration. This is then priced with a suitable margin and sold onto consumers. 
In reality can be a lot more complex. As funding comes from a variety of sources. Energy companies themselves can also be suppliers as well as providers meaning that they will both buy and sell a certain commodity on fixed price supply contracts.