SDP appeal rights. 

Does, or can a decision not to backdate an SPD come with appeal rights?

The Severe Disability Premium is a premium paid as part of a means tested benefit. The appeal rights will be the same as any other decision made on that benefit.

Usually in these cases, the question of backdating will be a question about the effective date of supersession i.e. the DWP will have superseded the award to include the SDP from date X and you say it ought to be paid from date Y. The effective date is set in law and you would need to refer to the provisions of the Social Security (Decisions and Appeals) Regulations 1999 to figure out if there is an earlier effective date which ought to have been applied.