If I go for it will the employer come to know from the NI contributions or by any other means.
No, certainly not by those means. Whether or not you have (let's call it) Job B will make absolutely no difference at all to the NI contributions to be deducted at Job A. Both employers will be required to deduct NI contributions on the basis of your earnings in that particular job.
But in a tax year there is a maximum amount of NI you need to suffer. If you end up paying too much then you can get back any excess over the maximum ... without either employer ever knowing.
Income tax! When you started Job B you clearly could not hand in a form P45. Neither could you sign one of the declarations on a form P46. This should mean that the employer at Job B should be applying code BR ..... a straight 22% tax deduction.
Again, after the end of the tax year, if you have not paid the right amount of tax then that will be adjusted direct with HMRC.
Finally Viren, your location is still shown as India. You might like to change that in your Profile, and you can easily get there by
clicking here.