Sounds like it could have an attack of red spider mite which suck the sap. You can get proprietary controls but they are expensive. Cheaper, but still not cheap is household flea spray from the vets, not the pet shop it is not effective. In the mean-time keep spraying with water especially under the leaves. They don't like water. Oh and spray nearby bushes as well. They are a true pest.

Red spider mite is very very rare outside anywhere in Britain and especially in this damp weather we have been having.
There are lots of critters which protect themselves with webs, from baby spiders to tent caterpillars. You need to search the bush for pests and then use an appropriate insecticide spray.

Most likely your bush is a Cotoneaster, and what you've got is an infestation of Webber Moth - two varieties of moth which infest these plants, produce the webbing, and the leaves turn brown because the larvae graze the leaves.
Treatment is usually to cut out affected parts, but if the infestation is extensive, then spraying is recommended - Bayer Sprayday Greenfly Killer or Doff All in One Bug spray should do the trick. Keep a watch next year - they overwinter and start their activities again in spring, but don't spray while the flowers are present. Google 'treatment for cotoneaster webber moth' and select the RHS page on this for more info.