Weighing in late
@Alexmac so apologies but been busy.
We run our 15t skiploader, most handy bit of kit on the fleet but also sporadic in it's use and arguably a burden rather than a money earner.
You need a O license to start.... Restricted is ample for your own stuff but you cannot move other peoples property. Get this out of the way long before you start looking at trucks. I can help you with working through the paperwork but not at this hour of the morning as my brain is already trying to slide out of my ear.
Lorry wise, if your only looking to move 6-7t weight machines and have anywhere moderately tight to go then go smaller rather than bigger. 15t is a much cheaper tax class, the payload isn't hugely different and a smaller lorry I find is better day to day.
Consider a tipper or hooklift. gives more options than a standard flatbed. Yes you need a waste carriers license and a place to tip if your planning to do small loads of muckaway.