Job offer received- JSA?

Hi all,

I'm very new to claiming benefits and wondered if anyone more knowledgeable might be able to help. Essentially, I left a job at Easter and have been claiming JSA and housing benefit. I've now been lucky enough to be offered a job but as the checks etc need to be completed its unlikely that I'll be starting for a couple of weeks. What do I need to do about informing the job centre? Also, can I claim JSA until I start, or do I need to sign off now?

Any help would be very welcome.

Thanks!