Moving to Berlin, working remotely for a UK company

Your situation is complicated in terms of tax and social insurance contributions, so you are well-advised to engage a professional (e.g. a tax consultant) to arrange things for you.
One thing is that, generally, you are liable for income tax where you live and work (i.e. in Germany, not UK) - no matter where/how it is paid out.
The other thing is that, without an employer in Germany, you are counted as self-employed, which has great implications on required paperwork and expenses. You must register as self-employed with the authorities, you must keep proper accounts and submit them to the tax guys, depending on what you do (and how much turnover you make) you may have to pay GST (MWSt in German) and, last not least, you have to pay both employee and employer contributions for compulsory social insurances -  for public health insurance alone this is around 15% of your income with a minimum of €340/month.

On similar lines want to ask if we come on jsv in germany and work remotely to employer in country of origin,is it legal,and its not violating immigration,jsv or other laws
if its not legal what is way to make it legal like if pay tax or other mandatory contributions in both countries if required

If you work remotely for a foreign employer or client who has no office in Germany and thus cannot formally employ you, you are counted as freelancer or self-employed.
This requires a different visa, a business registration, onerous bookkeeping and reporting rules and, last not least, much higher deductions for taxes and compulsory social insurances.
A JSV does not help you at all with all this.