I am starting an online jewellery business. The jewellery I sell will be handmade. And it's run at home. What type of insurance would I need for this?

As a new business it's great that you are already thinking about what insurance you need. There are a number of covers that may be useful, but to keep things simple you can opt to get them all included in a single business insurance policy.
 
Business equipment or tools insurance covers the things that help you run your business such as your laptop, your mobile phone, equipment, or tools for making your jewellery. Keep evidence of the things you've insured (like receipts or photographs) as this can help if you need to make a claim.
 
Also consider insuring the materials you use to make the jewellery, and any finished items you keep as stock. You should insure the maximum amount of stock you will have at any one time. If you're using precious metals or gems, bear in mind that it may be more difficult to find an insurer to cover you.
 
As an online business, postal insurance could also be useful, as it offers protection against items going missing or getting damaged in the post.
 
You should also think about public and products liability insurance, which covers you if your business causes injury to another person (not including an employee), or damage to someone’s personal belongings. This is still relevant for a business run from home, as it can cover compensation claims for injury or damage caused by the things that you’ve sold.
 
Also remember that if your jewellery business has employees, you are required by law to take out employers’ liability insurance.
 
As a home-based business you should also tell your home insurance provider about your business and what you're doing, as it may affect your home insurance policy.

See also: What insurance do I need for a home-based business?