Getting rid of ivy from a steep rockery

Gin_and_Milk

As someone who knows little about gardening, I'm not even sure if this is the right time of year to be doing this, but I need to be outside!
Our garden has been badly neglected. The small lawn at the bottom is cut when needed, but that's it.  At the top are two steep rockeries with steps in between ( which also has some plants left by the previous owner, but I want the lot gone).  One of the main issues is the amount of ivy, on one of the rockeries, mainly on the ground, but also growing up the fence.  It's also covering the tree, but as it's a sycamore I'm happy to leave it.
I've been cutting it back, and pulling as much out as possible, but because it's a steep rockery, some of it is very difficult to get to, and rolling it is impossible.  I've been cutting the stems wherever possible and sprayed those with weedkiller (although it rained about two hours later). 
I have heard of people using weedkiller, then covering the area with tarpaulin so that it will eventually die off.  Have any of you had any success with this?  If so, how long did you leave it on for?  I've seen some tarpaulin on Amazon, but thought I'd ask here first before jumping in.
Bizarrely enough, I'm actually quite enjoying it, even though I don't seem to be getting anywhere, but it's just not possible to do the whole area even with a ladder, as the garden is really uneven.

Thanks  
Gin

Justagardener

What weedkiller are you using?

Gin_and_Milk

Just an unbranded version of Roundup

Justagardener

Gin_and_Milk said:

Just an unbranded version of Roundup

That's no good for ivy you need a brushwood killer look up sbk brushwood killer online. It takes a while to die, so spray it and leave it alone. 2 sprays  will probably required 3 weeks apart. It will die don't worry

Grenage

I made a stronger solution of glyphosate and sprayed ivy where it wasn't welcome; it all died off in a couple of weeks.

Mojisola

If you can damage the shiny leaf surface the plant will take up more of the weedkiller.  If the slope isn't too steep, trample it.  Otherwise, get a big stick and have a bash.

Gin_and_Milk

Thanks for your replies, I'll look into getting the sbt stuff from Amazon.
What I haven't been able to reach I've been pulling down with a rake.  Not brilliant, but it's the best I can do!