In the UK there is no specific legal requirement to hold any particular type of "licence" to operate a digger, either on a construction site or elsewhere.
However, in order to comply with health and safety legislation, construction sites have to ensure that all of their operatives are trained and competent to operate the equipment that they are using. In the UK there are a number of different ways of proving this competency, with probably the most common being to hold a Construction Plant Competence Scheme (CPCS) card for the appropriate item of equipment.
Some sites insist that all digger operators hold a CPCS card, but the majority of sites will either assess operators themselves or they may accept any one of a number of other cards issued by various certification schemes which are running in the UK.
Diggerland has in the past run some Digger Driver Training Courses, but these did NOT provide a CPCS card.
We are no longer running Digger Driver Training Courses, but would instead suggest that you contact the CPCS, whose helpdesk number is 0844 815 7274. They should be able to give you the details for Driver Training courses in your area.