I would like to the same thing, and am having trouble, so I am interested in knowing too.

The only way I know involves elbow grease and a spade. I suppose you could hire a JCB if access is possible.

Pampas grass is elbow grease and fork/spade. Holly, cut right down, drill into the centre (if its a small trunk, 4 or 5 holes round the outside if large) with a medium wood bit, about quarter to half inch deep, fill up the hole with SBK (brushwood killer) WITHOUT spilling it on the ground or nearby plants, cover with something and leave (upturned flowerpot, whatever).

Hello Clem,
I can't advise on holly removal but pampas grass was great fun. Yes, elbow grease to start with, cut away as much as you can while protecting hands arms and face from vicious sharp leaves. Then on a dry day we hollowed out the middle of the plant and lit a good slow bonfire in the middle of it to kill it off. Felt very good and no noxious or expensive chemicals needed. You would just need to check with the council that your garden is in an area where bonfiring is not restricted or banned and even then be very courteous to your neighbours re washing lines etc etc.
Have fun!

We set fire to our large pampas grass one year and it came back mightily refreshed, in a horseshoe shape.

Not surprised Beattie, pampas loves being burnt, makes it stronger. Weeding's method of a slow burn would work though, but of course, isn't viable in lots of parts of the country - where I live, I'd be sued, its not permissible under the bye laws, as it isn't throughout most of London other than at certain times.

Yes I'm very lucky living here, any excuse for a bonfire! Neighbours bring their burnables round too so it's a very happy arrangement. I did see to it thoroughly that the pampas could not come back from the dead.