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I am replying to give you info about US. I do not know about UK jobs much.
If only applying and getting jobs were easy for non-citizens in US...
It is pretty hard to get jobs in US through consultancies now. Many of their visa applications get rejected. Depending on your education/work ex you could try uploading your CV in job portals like monster.com and dice.com for U.S jobs. Alternately, you could try for onsite oppurtunities from companies in India too.
I do not have any info on consultancies. You could try browsing the H1b forums of this website. You may find some info there.
I think for UK you will need to apply for HSMP visa. Check the pre requisites for it(I dont think you need a job forst unlike US visa). then, you could go to UK and search jobs once your visa is approved.