My understanding is that foreign lawyers from a common law country can take the bar exams in Washington state based on the information below.

Washington State Bar Association - The qualifications to take the bar examination are stated in APR 3 which requires the applicant to be of good moral character and to present satisfactory proof of:
(i) graduation from an ABA approved law school;
OR
(ii) completion of the APR 6 law clerk program;
OR
(iii) admission to the practice of law by examination, together with current good standing, in any state or territory of the U.S. or in Washington, D.C., or any jurisdiction where the common law of England is the basis of its jurisprudence, and active legal experience for at least 3 of the 5 years immediately preceding the filing of the application.
Here is the link : http://www.wsba.org/lawyers/licensing/bar_exam_app_info.htm

So I think the (iii) is applicable in my case.

My case:
I have done Bachelors of Law(LLB) from India. I have done LLM from Kent University in UK in International Commercial Law. I have around 4 years work experience. It includes working in the field of litigation in Indian courts for a year. Then, working with legal outsourcing companies (LPO) in India in US law (for US corporations and law firms) under supervision of a US attorney for 3 years.
My job functions with LPO's were - researching and drafting memorandums, summarizing depositions, contract review, document review (E-Discovery) , legal research using Westlaw and lexisnexis.
Would I be eligible to appear for bar exams in Washington state as I am from a common law country and have more than 3 years experience in the last 5 yrs?
Would the work experience I have constitute active legal experience both in litigation in Indian law in indian courts and legal outsourcing companies?
Would an LLM from UK help my job prospects in Washington state and towards my bar exam application?
Do I still need to do an LLM from US?

The Washington State Bar Association gives no guidance on what is considered "active legal experience". I can only speak from my own experience... I am an Australian admitted lawyer who just took (and passed!) the summer Washington state bar exam. I had been working in an Australian law firm from Feb 2006 - Oct 2009 (admitted October 06) and applied to do the Bar exam around March/April 2010.

Congrat ! How did you find the exam?

Thank you for sharing your experience. Congrats on passing the bar exams! Did you enrol in any bar review program to prepare for the bar exams? How long does it take to prepare for it? I heard barbri is good. Yeah the APR rule 3 is vague on what constitutes active legal experience. When I asked the WSBA about whether I qualify for appearing for the bar exams they said they will determine on basis of application. I hope they accept my application. I intend to apply for the bar exam in winter (feb) 2011.

I went through the same thing... The WSBA is quite unhelpful and you really just have to submit your application and hope that they find you eligible! You don't get your comfirmatory letter from the WSBA until 2 weeks before the exam so it is a bit of a stress. The application you fill out as a foreign attorney is different to the American law graduate one and you will need to very clearly specify what you have been doing for the past 5 years (including periods of unemployment etc).

As for the exam itself, for all the fear and hype surrounding it, it is really not as bad as everyone makes out. Having said that, there is A LOT to memorise. I did Barbri which I found invaluable. Full time Barbri starts about 2 months before the exam and I really didn't do any study prior to this. I found this time frame adequate.

Best of luck with it all!

The job market in Washington is, however, terrible at the moment.

It's true that it's not great (pretty much anywhere in the US for that matter). However I am in touch with recruiters who have a number of positions to fill as well as companies with in house openings. Then again, I am in the market for a 4th year attorney position. I have heard that there are fewer positions for the entry level attorney.