Prudential is a life insurance company, so the coverage is life insurance on you, not property insurance on your home.
I think it is common for banks to require this, but I do not have personal experience. Banks may also require property insurance on the home, but it is often limited to fire and related perils only, making it fairly inexpensive.
UOB and Prudential most certainly have an agreement to work together and have agreed policy wording for the claims payment clause which would pay the bank first for the amount of any outstanding loan. There will also be communication protocols between UOB and Prudential in the event of non-payment of premium. The bank won't want to have to negotiate these items with another insurer on a one-off basis.
The premium levels for the life policy are influenced by your age during the tenor of the loan making direct comparison with others more difficult.
Good luck.