It looks like sprouts coming up from a stump, but a better picture would make ID much easier.

Thank you all for the help. Yes, we have a sump pump, a very busy one. The uphill is behind where I stood to take the photos, the far end of the house has the walk-out basement door. We are re-grading, installing underground drains and have no clue as to whether foundation drains were installed when the house was built in 1975. We're guessing not because the sump pump was added in the 1980s. Already started or planned are several rain gardens to protect our downhill neighbor and decrease mowing. As for spoiling the appearance, I have a photo of how it looked when we moved in. The bottom branches were dead and irregular. Not attractive and a collector of stink bugs. What to put there is my next concern. I don't think I want a tree, maybe not even a large shrub. I've been reading that it's best to leave a bare area around foundation to decrease hiding places for the asian stink bugs (a big problem here, completely different than the west coast), gnats and ticks. Moving from central California has put me in unfamiliar territory. Year round rains, more bugs than birds, and a 50/50 shale and clay soil.

i see why they are there .. being invasive.. i would get rid of them ... but i would make it a multi year project ... starting at one end [or both ends] .. and planting something different ... while leaving the rest... to maintain some semblance of a screen ... and then.. each year.. removing another ... or just do it all at once.. and be done with it ... ken

I guessed you were in the UK from your use of the word 'garden' ;-) 1 & 3 are the arborescent (flowering) stage of Hedera helix, common ivy. You do not need to make an application to remove this. It is not a tree. And nor is invasive here. It is a valuable native species but a bit of a pain in a garden. 2 & 4 show a Privet hedge. Again no permission is required as it is not a tree. None of the pictures show Viburnum tinus and even if they did that is not a tree either. All you are doing is cutting back overgrown hedges and you do not need to get permission for that. I also live in a conservation area so I do understand the situation. However, the ivy appears to be partially growing up a tree next door so when you cut it back ensure you are only cutting the ivy and not the tree. If you want to remove branches of the tree get some closer pics and we'll tell you what it is.