Lab coats are required to be worn in all laboratories where there are chemicals in use. They are designed to protect your skin and clothes underneath becoming contaminated with chemicals including oil and grease.
They should not be worn with the sleeves pulled up as this leaves bare skin exposed to whatever you are working with. Similarly the buttons should be done up when in the laboratory.
There will be times when lab coats do not offer sufficient protection to you for the materials you intend to work with. Examples include fibrous materials e.g. rock wool, man-made mineral fibres, carbon fibre etc. These materials can penetrate into the fibres of the lab coat and lead to skin irritation and fibres getting into your own clothes. Some biological materials also require specific lab coats to be worn which do not have pockets and which do up to the neck (Howie). It is therefore important that you understand the hazards that you are working with and wear the most appropriate personal protective equipment (PPE) to protect you. This should form part of your risk assessment.
Engineering Stores do stock a number of disposable coveralls that can be worn over your lab coats. Tyvek coveralls for example can offer good protection against some of our fibrous materials that the School work with. Make sure you select the one most suitable for what you are doing. If we don't stock the right type, allow time to purchase the most appropriate for you and raise the matter with your supervisor/line manager.