What are your specific problems with Royal Mail? For sending out a 1st class large letter (i.e. your order) and it getting there the next day, Royal Mail is pretty great. Once you get into parcel territory they're extortionately expensive, but then the alternatives (if you're looking for CHEAP) can be like Yodel/Hermes and bring their own problems.
I suggest talking to a franchise company like InXpress (not affiliated!) who have great packages with all the courier companies and can handle everything for you.
But if most of what you send out fits into the parameters of a Royal Mail large letter and you don't have any volume to speak of yet, I don't think you're going to find a better alternative.