That's a good thought, Alina W. Thanks.
I have just been out to take another look and measure the circumference of the trunk. It is about 45cm around, and the trunk is not actually leaning, as I first thought, but is the shape of a shepherd's crook. All the branches are at the top, so it gives the impression they are being thrown forwards. The optical illusion of falling seems to be further magnified because it is at the foot of a very steep bank. I find it really quite disconcerting to look at - perhaps because subliminally it makes you think of somebody about to jump off a cliff, or something like that. Hard to say, but it just looks WRONG. 
We have tried to straighten a wonky gatepost of a similar size using ratchet straps, so I have a pretty good idea that trying to adjust a trunk of this size by means of ropes might not work all that well!
I think that once we get into the colder weather and it starts to go dormant I will have a go at cutting the side branches back fairly hard and see what happens next year. If all else fails, there's always the chain saw the year after, but we have had to take out so much from this garden since we moved in that I am now trying to conserve, where possible, rather than pull up or chop down.
Perhaps I can make it into a topiary Tom Daley? 