Interesting to see some US in there! How can they legally work in the UK? UK immigration is a mess right now [1]. I would know, I barely got in on my Tier 1 - which no longer exists [2][3].
Because if they find out you're lying (or, indeed, suspect you're lying) and deny you entry, you'll forevermore have trouble getting in to the UK.
Place I worked at during the late 90's had the UK immigration folks turn up and tell a US citizen on a tourist visa to get out of the country. He was working illegally on a tourist visa while he was waiting for his work visa to be approved. Suffice to say the work visa never got approved after that.
The brother of a friend of mine from Oz went to the States and somehow ended up joining the circus as a carnie where he worked illegally for a couple of years. He was caught when the circus went in to Canada for a while and they checked everyones papers when trying to reenter the US. He was denied entry, got banned from the US for 10 years and the rest of the circus waved goodbye and left him at the border.
Totally worth it just for having such an adventure for a couple of years.
[1] - http://www.economist.com/node/17581736?fsrc=scn/fb/wl/ar/the...
[2] - http://www.ukvisas.gov.uk/en/howtoapply/infs/inf21pbsgeneral...
[3] - http://www.ukvisas.gov.uk/en/aboutus/newsroom/?view=News&...