Looks tree like, doesn't it - not a sucker off the lilac then?

Could it possibly be a dogwood? Perhaps a sucker from something on the other side of the wall?

The lilac leaves are heart shaped, Bamboo, so not at all the same.

I wondered if it could be a seedling or shoot from a Philadelphus. There are a couple about 10 feet away. Would it be this vigorous, this young?

The other side of the wall is a garage interior, so I can't see the plant coming from there (but it's someone else's garage so I haven't looked inside).

There's what I think is a dogwood about 20 feet away. Do they produce seedlings?

From the position, under a branch, it could have been a present from a bird?

It's got the look of a hazel about it, but i'am more likey to be wrong, if i am sorry give me a smack on the back of my hand

I thought hazel too. ceratinly probably self sown.

Beattie, better get round next door and check out that garage lol.

LOL - the Triffid-garage! :-)

Perhaps it'll flower next spring, then it'll be easier to identify, Beattie. Is the main stem very twiggy and hard? It does look like a dogwood, the way it's growing with tall, straight stems. Not much help there, then! Annie

Better move it as what it is, as its a bit near the wall isn't it. Don't throw it though as by now we all want to know what it is!

The leaves are opposite, so that is consistent with Lilac, Philadephus, and Dogwood, but not with Hazel. The venation on the leaves looks like a kind of Dogwood, though they are distorted, like sucker's foliage frequently is.

Thank you all for your thoughts. I think I'll advise getting it out, whatever it is. The option of growing it on in a pot is one to consider - if only to satisfy my curiosity. :-)

I've updated the question with some more photos including one of a nearby shrub for comparison. Any chance of naming THAT one?

Philadelphus was my first thought before I read everyone else's ideas - really don't think it's lilac

That last picture you posted - are there two plants growing there? Its just that at the top towards the right, there are leaves and possibly small pink flowers that resemble some kind of Viburnum.

You're right, Bamboo, there are 2 shrubs close together. I recognised the Viburnum as it was helpfully flowering, though I don't know which species it is.

The similar waviness of the leaves in pic 1 & 2 make me wonder if they're the same.

The other leaves mixed in with the Viburnum remind me of Leycesteria...

Interesting point, Bamboo. I'm very used to pulling out unwanted seedlings of that! There could be no flowers because of "trimmer man", and the leaves are quite like... I'll go and see if the stems are hollow.