I am quite annoyed with my new company and upset with myself for rushing to hand in my resignation

Seen the ad for job from new company on internet and applied the same day- 30/12/2014
Ad start date 22/12/2014
Ad closing date 23/01/2015
called/emailed on 26/01/2015 to say i have an interview
Interview date/ tests- 29/01/2015
Confirmation of selection - 04/02/2015
Based on the confirmation I handed in my resignation to my current employer on 04/02/2015 evening (expected them to say you have to serve notice period etc..) and they came back to me the next day and said they don't even expect me to serve the notice period and can leave immediately if i wanted to, and they told me they will pay me 4 weeks of notice without working for them. It all sounded fine. Now i have started to liaise with my solicitor and and looked at the COS issued by the new company. Everything is fine, when i looked at the RLMT - they had put the ads on job center plus and indeed. Job center plus doesn't have a closing date , though on indeed where i applied it had a closing date of 23/01/2015. So i called the company to query on this as now my position is quite bad and they told me they will be taking the adverts off the website on Monday and when i go for the visa, home office cant check details but they can only see details of ads on the COS. But they had put the jobs ref, date posted etc on the COS and they also told me on job center plus they had put the closing date, but it wasn't visible at all for some reason. Also they told me they had done exactly same process for 2 other employees they had hired on tier 2 and they had got their visas.
Also the new employer said, they had home office compliance visits last year in june and they were happy with the way RLMT was conducted for other staffs and assured me theres nothing i need to worry about.
also am i correct in assuming my 60 days start from 05/02/2015 as my current employer would have reported this? They havent come back to me yet on this, but i am just figuring out.
Please advise i am overall quite worried right now.
Regards
Vimal