No, the rejection of a Schengen visa has no direct bearing on any application for a UK visa. Every application for a UK visa is treated individually on the basis of all facts available to the ECO at the time of assessment.

Does the UK have access to the records of Schengen visa denials - YES. If you fail to disclose that refusal, new passport or otherwise, they will find out and then you will not only be denied the UK visa, but also face a potential EU-wide ban for a longer duration.

Any visa agent who advises you to get a new passport or to conceal information is not to be trusted. A good visa agent will advise you how to frame your true circumstances most convincingly to overcome potential questions raised by the ECO. For example, if your Schengen visa was rejected due to a concern that you might illegally immigrate, your UK visa application should focus on providing evidence of ties (family, property, business, job offers, etc..) back in your home country that make it more likely for you to return after completing your course.

All said, I will reiterate again that whatever you do regarding the new passport, DO NOT CONCEAL YOUR SCHENGEN VISA REFUSAL on the UK visa application form. I know of too many young people who have had their careers irrevocably changed because they took bad advice and wound up getting caught in their lies.