I think I've read every possible post on this web site (and nearly every other government/official/unofficial web site there is.) Not a professional of any sort, I can help you find the information you need. However (to reiterate what others have said above) noting that you want to go for a relatively limited amount of time, its probably better just to save up. As another poster said, company's wont invest in someone who will stay such a short amount of time. If you go over there and work under the table or illegally, you could jeopardize yourself as you could be refused admittance into the UK. If you really want to travel (and I've backpacked nearly everywhere), there are always low cost options (like hostels) and cheap ways to get by even in the most expensive of places. Also, not working gives you the option of leaving and going from place to place of your own accord.
With that in mind, below find some information that you might find helpful on your quest.
1) Recently Delara posted an excellent summary of the different ways to get a work permit. You cannot get a visa/work permit without:
a) a student or within 6 months of your university graduation through www.Bunac.org and this visa is only valid for 6 mo.
b) an allowed "repeat offender" to the above organisation
c) married to a UK citizen having gone through all the proper channels
d) highly skilled and have an HSMP
d.1) highly skilled in a job that is in desparate need (i.e. nurses, doctors and teachers with proper qualifications)
e) not highly skilled and get that Hospitality visa (only allowed to work low wage hospitality jobs) -- not sure if this visa is still offered
f) highly skilled and sponsored by a company
g) transfered by your present company
h) can prove you support yourself as an artist/writer/musician etc
i) have dual citizenship with a Commonwealth country and get a WHV (working holiday visa)
j) ancestral ties (parents/grandparents)
k) born in the UK but grew up in US, thus able to get a passport
l) born in any other EU country, thus able to get a passport in said country and work in UK
m) oh yeah: enrolled in university in the UK and thus given a student visa (restrictions on how much you can work)
The Home Office web site is another great source of information, though the navigation is a bit strange. Through this link, you can get to the information on the different schemes available:
http://www.ind.homeoffice.gov.uk/working_in_the_uk/en/homepage/schemes_and_programmes.html?Good luck.