I want to register my home address as my company address (it will be a limited company). Do I have to inform the landlord and do I have to pay any extra tax?
The registered office is an administrative matter so a landlord does not normally have to be notified. It is akin to working from home which does not fundamentally stop the property being a 'home'.
There is no extra tax payable so long as this principle applies and the use does not change.
Some modern developments include 'live/work' units where planning rules permit part of the property to be an office. The difference is often difficult to judge but is generally a degree of scale. The more visitors you have and the more commerce that is transacted from the property the more likely it is to be judged an office and treated accordingly for business rates and tax.
A resident can choose to designate part of their property as commercial space but that should be cleared with the local planning authority first. A use limited to a few visitors and a small room is usually acceptable. The benefit is that part of a mortgage for the property becomes tax deductible. The downside is that you lose Capital Gains Tax main residence exemption for that part of the property. An accountant would be able to advise in more detail on the pros and cons.