You may have to try pruning it back in stages - certainly they can be pruned, and quite a bit, but if you wanted to remove half or more of the growth all at once, probably not such a great idea. You can certainly quite easily prune it to keep it a cone shape and prevent it getting so tall and wide again, but not sure about a lollipop effect, they tend to have lots of stems coming up from the base rather than one central 'trunk' with growth coming off, though its possible yours hasn't because you've not kept it pruned. Plus you'd still have to keep the top pruned, or it'd grow back into a taller, wider cone shape (its natural growth habit), which might look quite odd on a single stem. Either way, the time to prune these is absolutely not now, but around May/June time, to give the plant plenty of time to recover before winter arrives.

Thank you for your reply Bamboo, my tree does have one central trunk, so I'll probably try to cut back a bit of the lower stuff after the birds have finished nesting in it early next summer. Nothing too drastic though!

I also have a big one about 12-14 feet high and quite wide and it also has a central trunk. I dont think it would suit a lollypop shape as its beauty is the foliage all the way up and its natural conical shape may well look top heavy and very odd.
3-4 years ago mine looked a bit sick so I cut off every leaf and reduced a lot of the twig like branches, tidied it up but kept its conical shape. gave it a good feed and mulch.
It looked very bare for 2 years but fully recovered and looks great. This spring and again this week I gave it a light prune to maintain the shape and size.