In light, workable soils, cut back the scrambling stems to around 30cm (1ft) from ground level. Strimmers will deal effectively with large areas of woody weeds.
Dig out the bramble stump, taking the roots away at the same time. It is important to remove as much of the below-ground parts as possible, as brambles have the ability to regenerate from well below soil level. Seedlings should be weeded out by hand.
Stems and roots shaken free of soil can be finely shredded and used as a mulch. Alternatively they can be taken to a local council green waste facility or burnt in bonfires. However, bonfires create pollution and may also annoy neighbours. They should be conducted when wind and weather mean that smoke will not enter houses or inhibit others from enjoying their garden. Here are some government guidelines on bonfires in smoke control areas.
Cut back all long, trailing stems to within 20-30cm (8in-1ft) of soil level, and deal with as above. Immediately afterwards, apply a suitable weedkiller such as triclopyr (SBK Brushwood Killer) or glyphosate (tough formulations such as Scotts Roundup Ultra, Scotts Roundup Tree Stump & Rootkiller, Bayer Garden Rootkill Weedkiller or Doff Maxi Strength Glyphosate Weedkiller) to the freshly-cut ends of the stems, thoroughly wetting them to ground level, following the manufacturer's instructions.
SBK Brushwood Killer contains a selective or growth-regulating weedkiller (triclopyr) which breaks down in the soil within about six weeks. It controls most broad-leaved weeds and young woody saplings. It does not kill grass, though some damage to lawns and fine turf may occur. It is effective applied to the foliage of woody plants such as brambles from spring until autumn.
Inclusion of a weedkiller product does not indicate a recommendation or endorsement by the RHS. It is a list of products currently available to the home gardener.
Weedkillers for gardeners (Adobe Acrobat pdf document outlining weedkillers available to gardeners; see sections 1a and 4)
Chemicals: using a sprayer
Chemicals: using safely and effectively
Chemicals: using spot and broadscale weedkillers