Oh dear, a marathon task. The answer is a painstaking labour of love, I'm afraid, so here's what I'd do. First, you'll need at least one bottle of SBK, a brushwood killer. Cut down the lilac, either poison the stump or have it removed by a tree surgeon (they have someone who'll come out with a treestump grinder which will remove the roots down to about a foot). Cut down the buddleias to the ground, or to a nice bit of thick, chunky root. Dig around any suckers from the lilac, hopefully revealing some nice chunky, woody root again. Now drill into any stumps, large and medium woody roots with a medium sized wood bit on a drill, to make holes a quarter to half inch deep, depending on the size of root. Fill up the holes with the SBK (don't spill it anywhere, use it neat, wear gloves), cover with an upturned flowerpot or a piece of slab or even a plastic bag, whatever's appropriate. As for smaller roots which aren't big enough to drill, hack into them with sharp secateurs or loppers, even a sharp breadknife, pour the SBK over the cuts you make, cover again. If the roots you treat are deep in the soil, use an old flower pot upside down, replace the soil, leaving the pot in place. This excludes soil and nutrients, and enables you to find the roots again if you need to retreat.
Keep any eye out for buddleia seedlings over the next few years - they're opportunists, and will seed themselves readily (you've only got to look at disused railway sidings for proof of that). Get them out while they're small.
I know it all sounds like hard work, but it does resolve the problem - its one of the things I've consistently had to do in clients' gardens over the years, so you're not the only one with these kind of problems, if that's any comfort, lol!

Well now Sarah, we do seem in a pickle, it seems you are quite angry about all this nature overtaking your plot. However, help is at hand. My contribution to your question is to suggest some meditation in amongst your jungle mayhem for starters & before you pick up that spade to clonk me on the head with it quite simply that means just taking a cup of tea into the garden & think 'systematic' & try not to get 'overloaded' by the tasks ahead.
Sounds like a major overhaul is required, this takes time & if you have someone to take on the work it will get done to your satisfaction.
Those terraces look really nice & already I can see new plantings overhanging the walls whilst the existing 'good' plants will benefit from a quick trim to neaten them up.
As for the root eradication this is plain 'elbow grease' in the main but there is plenty of good advice coming your way on this subject I feel sure.
Dont let it get you down Sarah, it's going to be superb as you seem determined to change it.
Just try not to resort to dynamite ;-)

Yes, a big job. But remember that shrubs can't grow in lawns, so cut off all shoots every week (as if they were growing in a lawn that was being mowed every week) and eventually they will die.

when you said 3 problem areas I thought hips bum and tum [in my case not yours :o)]
This is going to be a long term project here and you have been given soe good advice here too.

Don't fret Seaburngirl - hips bum and tum become a problem of the past when you get up the wrong end of 50 - then its abdominal fat and bingo wings instead...

but i am the wrong side of 50 :o(
and i have the tummy but not the wings!