As already mentioned, yes you do need to have the 'Road Fund Licence' (also known as 'car tax') paid, and you need at least 'third party' insurance, to cover damage you may do to any other vehicles and/or their occupants.
As also mentioned, the insurance can be extremely expensive, in some cases costing more than the car itself (especially true if you buy a cheap second-hand car).
Another answer mentioned the MoT (Ministry of Transport) test. This is required, along with the insurance certificate and the car's registration document, in order to get the 'tax disk' that you get when paying the road fund licence.
Because of these requirements, it is very important that you select a car that will not cost you too much to earn, when you do buy a car. Be careful to buy one that has a long MoT certificate (6 months or more - preferably more!), and that is in a lower insurance group. Get insurance quotes from several companies before you buy the car, to make sure you have a good idea of how much it will cost before you buy something that you can't afford to insure.
For this reason, older cars that were once expensive, luxury or sports cars, tend to have a much lower second-hand value, since they can be expensive to get through the MoT, and can be prohibitively expensive to insure.
Also - when buying from a garage, it can be a good idea get the car inspected by a third party to make sure that it would REALLY pass an MoT test. The 'conflict of interest' works both ways, and an unscrupulous garage might give an MoT certificate to a car that would not have actually passed a 'proper' test, in order to get rid of it.