No only one licensed copy per machine. If you want to use XP on both machines you'll need another license. If your drive is partitoned or a dual booter you can still use XP as its all on the same machine.
Additional licences can be purchased from MS at a slightly reduced cost for the second copy.
If you try to install the same copy on a 2nd machine, you will be unable to activate it, as the code will have been registered on the first PC. If it is not activated, it will not run after (I think) 30 days.
Even if you could do what you want, it is very rare for commercial machines to have a full copy of XP O/S provided with them. Normally it is a "recovery disk" or some such euphemism or sometimes no disk at all.
Evesham doing this admirable thing (I do mean that, it's not a sarcastic comment) is an exception. Most suppliers do provide only one of these half baked things or nothing at all without charging extra - and the only supplying a recovery disk. Tiny/Time/Computer World (or whatever they're called now) come to mind in that.
If your supplier is using a standard OEM version of XP, ask him if he will supply a second copy at a low rate (you are, after all buying a whole machine from him). You can then use that on your current machine. Remember to do a full fdisk and format beforehand though.