How brutal can I be

That looks like Portugese Laurel to me FC ,If it is it can take hard pruning late spring early summer so any time now should be OK but wait for back up to confirm

 

I'm no expert though I'd agree with loli.
When I saw the title of your post I though, oh-no. I tried to prune a rhodo once, very gently, but it ended up an unsightly lopsided mess and never really recovered.
With a better photo it would be easier to confirm, but if it is a laurel it will take a fair bit of terrorising, if you get your head inside for a look around at the structure and bushiness inside you will be able to make a better job of the pruning (though it still may look a bit rubbish for the rest of the season).

Hope you are feeling better.
GG

 

That should be fine FC. I think you've chosen a good pruning point and at least give it a shape of some sort. You may be lucky judging from the photo in being able to cut back the tall points which appear at the back near the fence, that way you will still have a nice 'front'. Once done, I would trim it to keep it at the desired shape late spring and autumn then it won't get out of hand.

GG

 

Has it got a nice trunk (or two/three) on it ? If so what about cutting all the lower growth under and to the right of your red line off level with the fence and then you'd claim your garden back and you could grow a Clematis through it.

 

That's a good job done. More or less what I suggested

 

Good pruning job ! That one is a Prunus laurocerasus, Cherry laurel.