My question is about tax and NI when your salary changes. With my old job/salary my total deductions are roughly £400. With my new job deductions come to £500, however these figures come from the "listentotaxman" calculator and are based on the annual salary. Does this mean my actual deductions with my new job will be somewhat less than the higher figure (to begin with?) If not , how do I get the correct figure?
Your PAYE tax code should not change assuming you don't have a gap between employment or you are not going from lower to higher rate taxpayer your employer (via your p45) and HMRC should sort this out for you.
I am not sure what you mean by "deductions" here and woudl suggest not going random dodgy sites on the internet I would suggest going to the HMRC site and using the tools provided.
However you should check your Tax code on your first pay slip to make sure you are on the correct code and haven't been put on an emergency code by mistake.