There are no licensing requirements which apply specifically to furniture manufacturers.
If you sell goods direct to consumers and you offer them finance then you will need consumer credit authorisation from the Financial Conduct Authority (FCA). For more information visit the consumer credit section of the FCA website.
Depending on the scale of your business and how you operate, you may well need one or more reasonably large delivery vehicles. If your business operates goods vehicles with a gross plated weight of more than 3.5 tonnes (or unladen weight more than 1,525 kg for unplated vehicles) then it will need a goods vehicle operator licence in England, Scotland and Wales. You must have an operator licence for each Traffic Area in which you have a base. Licences are issued by the Traffic Commissioner for that area. There are eight Traffic Areas covering England, Wales and Scotland. In Northern Ireland you may need a goods vehicle operator's licence from the Transport Regulation Unit (TRU) of the Department for Infrastructure (DfI). More information about goods vehicle operator licensing is available on the Gov.uk website - and from the DfI in Northern Ireland.
You should also be aware that businesses that keep records of individuals' personal details - perhaps for finance purposes - may be required to register as data users with the Information Commissioner's Office (ICO). From May 2018 the General Data Protection Regulation has introduced additional protection for personal data. You may also need to register if you use CCTV equipment.