These are not spider webs as you may have first thought but protective webs spun by the larvae of the Hawthorn Moth, Scythropia crataegella. This 10-15mm moth is common in Leicestershire and Rutland. The larvae feed on Hawthorn and Blackthorn but in urban areas where these food plants are not around they take advantage of Cotoneaster horizontalis. The inconspicuous larvae are leaf miners but when they are ready to pupate spin these protective webs. The Royal Horticultural Society gives advice on this, saying "The foliage becomes brown and dried up where small, dark brown caterpillars have grazed away the leaf surface, giving the impression that branches have died, however affected areas will usually produce another flush of leaves and recover... Whilst the appearance of this pest can be alarming and almost all of the foliage can become covered in webbing and turn brown, the plants usually recover without treatment and so control is not always necessary". So put away the toxic insecticides and enjoy the Hawthorn Moths.
Hi Alan, since the article about the cobwebs, I have noticed caterpillars and cobwebs on some spindle twigs.
If you can get some photos we can try and identify them positively. Knowing the host plant is often a big help.
Hi Alan again, I have no means of taking close-up pics but can leave the caterpillars to develop on the spindle, unless they get picked off by birds. No idea how successful this will/will not be. There are not as many twigs affected by the cobwebs as in your pic.