There is no licence for this machine.
No UK government body issues a licence to operate a roller, and no statute requires one. The duty to train and assess competence sits with the employer, under the Health and Safety at Work etc. Act 1974 section 2(2)(c) and the Provision and Use of Work Equipment Regulations 1998 regulation 9.
This training is structured operator training with formal theory and practical assessment, which the employer can rely on as evidence when meeting that duty. Sites may set their own entry requirements, and the operator should check with the site before attending.
The controls that matter are the same as for a dumper: the roll-over protective structure (ROPS) and the seat belt.
The Control of Vibration at Work Regulations 2005 apply to whole-body vibration. The Provision and Use of Work Equipment Regulations 1998 apply, and HSE guidance HSG144, Safe use of vehicles on construction sites, sets out the wider standard for site vehicle use.