I suspect that Nick meant baking soda rather than baking powder. It is commonly recommended for cleaning coffee stains from mugs and coffee makers.
Which brings up an important point - descaling boiler internals, and cleaning of coffee residues are two very different processes that should not be confused. To you clean your portafilter or the inside of your dispersion screen you need a detergent that dissolves coffee oils. You don't have coffee residues inside your boiler, and you don't normally clean it with detergent. But when it is building up a little limescale you need to dissolve that with an acidic descaling solution. You can buy compounds for either function. (You can even buy yet another detergent that is formulated to clean milk residues) and you don't want to confuse them.
For descaling a Pavoni, a 50% white vinegar solution is often recommended. You fill the boiler with that, then let the thing heat up and sit an hour or two, flush a little of that solution through the group, then cool, drain and inspect, and repeat if you still have scale. Finally rinse and rinse til all the vinegary odor is gone. You can also use a citric acid solution (one tablespoon of citric dissolved in 1 quart of hot water.)
See How to descale chrome components without damage?
for a Pavoni owner / chemistry professor's discussion of vinegar vs citric acid.
I now see that the OP is in the UK, and in my earlier post I recommended a couple US shops for parts. I'm sure there are similar shops in the UK that sell Pavoni kits and parts, just don't know which to recommend.