At 1cm long, this cannot be long out of the egg, as they will get up to 3.5cm long before pupating.
This is the Vapourer Moth Caterpillar - very distinctive, but if you are in any doubt, remember the 2 dark "horns" at the front end, and the blindingly obvious 4 cream "shaving-brushes" down its back.
As is very often the case in Butterflies and Moths, the dullest Moth often has the most extravagant, showy caterpillar - the most beautiful Butterfly or Moth often has a very plain caterpillar. The Vapourer Moth is no exception to that rule, as can be seen by the photo of the adult male (only the male Vapourer has wings - the female is little more than a bag of eggs) below (taken from the WAB site), but what a fantastic pair of feathery antennae! (Butterflies as a rule have clubbed antennae, Moths - feathery).
Vapourer Moths are very common in towns and cities - I found one in Oxford Street once, in a tiny tree outside that bloody awful, massive John Lewis store. (The tree was FAR more interesting than anything inside the building)!
Vapourer Moths are considered to be somewhat of a pest in some "leafy cities".
One last point about the Vapourer Moth is that is does have a good scientific name - Orgyia antiqua. The Antique-Orgy Moth then. Easy to remember.
NB. 23/06/07 05:00am ... less than two days later (more like one and a half really), the same Vapourer Moth Caterpillar on the same plant, and probably TREBLE its size of almost 2 days ago - at 3cm long. Greedy little chuffer.