The Gov.UK site for permanently settling in the UK ("indefinite leave to remain" or "ILR") lists out the fees associcated with the application, but not the payment methods accepted. For instance, do they take card payments from both credit as well as debit cards?
I was unable to find a govt.uk webpage which addresses how payment is to be made when applying for ILR.
The govt.uk webpage that addresses ILR-holders applying for UK citizenship, however, contains this text:
How much it costs [sic]
It costs £1,330 to apply.
You must also pay £19.20 to have your biometric information (fingerprints and a photo) taken. You’ll be told how to do this after you’ve applied.
It's very likely that the "apply for ILR" procedure is similar, and that sometime after you've begun your application for ILR, you'll be advised how payment is to be processed.