No, not British, I'm in South Africa
Although parents accompany their kids to pre-op, and are present during induction, an experienced nurse must be present in the pre-op area as well. There are various excellent reasons for this:
1 - The patient may injure him/herself while confused.
2 - Possible unexpected reaction to the premed, which may include mild to severe allergic reactions, nausea & vomiting, excessive drowsiness and depressed respiration.
3 - Any patient scheduled for surgery is anxious; even if the child is too young to understand what is happening, it is extremely traumatic for the parents. Add to that the fact that most people have read or heard of horror stories involving anaesthesia and you realize that despite their outward calm, those waiting in the pre-op are in a state of suppressed fear. A professional, informed person should be at hand to answer questions and at least partially allay these fears. Where adult patients are concerned, it can even make a difference to their stay in recovery if they are less nervous going in than if they're left to stew in their own juice in pre-op.
As regards monitoring vitals pre-op, we don't commonly do it, but we have a sats monitor and dynamap in the room, and of course oxygen and suction equipment is close at hand. Strictly speaking, all pre-ops should be equipped with O2 outlets and suction points, but due to design flaws, we've had to make do with mobiles.