Took few pain killers for back. can i drink coffee 1 hr later ?

Yes, but . . .: It would've been useful to know specifically what you took that you're calling a pain killer since there are many types available. Good news is that most, if not all, are not affected by coffee. However, this should've been something that your prescribing doc told you at time of your visit. If this is a non-prescription over-the-counter pain reliever, then none in States are problematic tho in UK?

Yes: There are no interactions between the caffeine (in coffee) and the active ingredients in most any conceivable drug you may have taken for back pain.