A note of caution: It is not always possible to transfer from one university to another part way through a degree. Whether this can be done will depend on individual circumstances.
Obtaining an LLM might but would not necessarily make a candidate for jobs in the legal sector more competitive.
What type of job would you like to do?
Please note that working as a barristers' clerk, whilst an important job which many find interesting and which is (eventually) well paid at the top end, doesn't lead to qualification as a lawyer. Barristers' clerks are the sales, marketing, and administration/support element in a set of chambers. The role of a junior clerk is poorly paid and laborious. There is a lot of photocopying, tea making, and trolley pushing.