After years of neglect the bottom of our garden has loads of suckers and a shit load of ivy mingled with spiky blackberry type vines.
Short of salting the whole lot, any advice on taming the jungle?
Machete.
You could use a strong weed-killer but the best way is to roll up your sleeves and start by cutting down the thick growth so you can see the ground.
Next dig out the big weeds making sure you get the roots out. Brambles are a pain as they have deep, thick roots. You may need to do this several times.
Break up the soil with a fork to make it more manageable.
Once you have the big stuff out then use a dutch hoe to skim under the weeds and remove the roots. Rake the disturbed weeds out with the back of the hoe or a rake. Remove them and put them into the bin.
If you've got this far then it's going to be a regular job as the weeds will come back. Some of the larger weeds will not like being topped each week so just strim them back until they give up. However many weeds will keep coming back and you'll have to go through this process over and over again.
One tool that I find good is this one.