Could you tell me what documentation I would need to visit Las Vegas if I'm a UK citizen currently working in Mexico City?
Assuming you're flying, and that you're visiting for tourism or business, you need valid ESTA authorization and the passport to which your valid ESTA authorization is tied.
You may also be asked to show evidence of your immigration status in Mexico, but of course you'll have that with you because you'll need it on the return journey. There are two reasons for this, but one applies only to subsequent visits. The first reason is that an air ticket from the US to Mexico only satisfies the statutory "round-trip ticket" requirement if you reside in Mexico. The second is that on subsequent visits you may have to show that you reside in Mexico because that exempts you from the rule that time in Mexico does not reset the 90-day period of admission under the VWP.
If you're crossing the border by land, you don't need the ESTA authorization. If your visit is for reasons other than business or pleasure, you'll need a visa of the appropriate category.