I'll be working from abroad (I'm in the US and going to the UK) for about a week. I'll be spending my days 8+ hours working, and spending the nights out.
Can I deduct the plane ticket for this trip as a business expense?
It depends on what the "true" reason for the trip is.
If you decide to deduct the trip as a business expense, then during an audit you will be asked why you had to go there. If there was nothing accomplished via the travel (that is, you worked from the hotel, met with no clients, visited no tradeshows, etc) then the expense is unlikely to be allowed.
Yes, on a business trip you can do sightseeing if you wish (though you can't deduct any sightseeing specific expenses, like admission to a tourist attraction), but if you are just working while on vacation, then the trip itself is not deductible, since there was no business benefit to traveling in the first place.
The relevant IRS publication is pub 463. Note that there are various conditions and exceptions, but it all starts with business necessity.
Is it necessary for you to work from the UK? If you're working from the UK because you wanted to take a vacation, but still have to work, and would do the same work without being in the UK - then you cannot deduct travel expenses. It sounds to me like this is the case here.