I know that the majority of the hills and valleys in Scotland, north England and Wales were formed by glaciation, and the rivers that then followed those paths. Based on that I would make the huuuge assumption that without ice, those "indents" into what was once the surface level of the ground would never have been made. This would give large and high plateau areas instead.
Another interesting thing to note is that since the ice of the last ice age disappeared from Great Britain, it's northern end has been "bouncing back" due to the absence of the weight of the ice. That is, the northern end of the island is gaining altitude, whilst the southern end is effectively sinking into the sea in balance. Without the ice, this also would not be happening.
Without the ice, the British Isles would also most likely still be joined together (one British Isle, singular), and probably also still joined to Europe as your lovely diagram states. This would likely have rather huge effects on the biodiversity of the Isles, the path human development and their cultures took, and all historical events that have resulted since human settlement.
Edit: To clarify, the separation of the British Isles from mainland Europe is thought to have occurred due to "two catastrophic glacial lake outburst floods" caused by the breaching of an extremely large lake under what is now the North Sea. This is not ice directly on the British Isles, but arguably the removal of that ice contributed to the breaching of the lake.
Pretty big hypothetical you got there.