Which council issues your permit?
Reading's built-up area runs across three councils, and the permit for a skip on the road comes from the one covering the address, not the postcode town. Central Reading is Reading Borough Council. Earley and Woodley are Wokingham Borough Council. Calcot, Purley and Theale are West Berkshire Council, and Tilehurst is split between Reading and West Berkshire.
The skip company applies for the permit whichever council it is. Ask whether the cost is included in their price and how much notice they need. A skip on your own drive or private land needs no permit at all. See the skip permit guide for how it works.
Terraced streets and tight access
Much of east Reading and the streets off the Oxford Road are Victorian terraces with no off-street parking and cars parked on both sides. A road permit is the normal case there, and a full-size builders skip may simply not fit the space available. A mini or 4 yard skip is often the practical answer, and it is worth describing the street when you enquire.
Choosing a size
For a kitchen or bathroom refit an 8 yard is usually right where there is room. For soil, rubble or a patio lift, stay at 6 yard or below, because weight rather than volume is the limit. The size guide works it out from what you are clearing.