You say that the only way to find work is to start by claiming job seekers allowance – I find this statement ridiculous. You can actively search for jobs without necessarily claiming for benefits.
However, you can receive a lot of helpful advice and information from your local Job Centre, as well as assistance with training to get you started at work and I would strongly recommend that you visit.
You can apply to receive JSA if you have the right to live and work in the UK, this is all the information you need to submit your application for JSA. They will tell you what is required in order for your payments to continue including actively searching for work and attending your interviews and appointments with the JobCentre.