I use a Glyphosate based weed killer for everything, buy it in the concentrate form so can mix it up to the required strength myself. only thing is that it's a non-selective herbicide, so will kill everything.
When just spraying grass and young broadleaf weeds (before they've developed a thick waxy layer (cuticle) on their leaves) mixing at 1 litre per hectare works great. However when there's more meaty stuff to kill, I mix at the maximum reccomended dose rate....5 litres per hectare.
With this i've managed to wipe out small tree (ash, sycamore, oak) saplings, ground elder, weeds over 4 foot tall, not found anything that survives a good dose of this. A small squirt of detergant in the mix also helps as it breaks down the waxy layer on the leaves....allowing the chemical to be absorbed better.