You have very limited rights in these circumstances. Your employer is not obligated to allow employees to have any smoking breaks at all, and is legally required to prevent employees from smoking in the workplace. As such, your employer is acting in accordance with legal requirements to prevent employees from smoking on the work premises.
It is not clear from your question if you are the only employee on shift. Generally, employees working a shift of six hours or more are entitled to a 20-minute unpaid break during their shift. The entitlement is to one break only and you can normally take this away from your workstation. However, there is an exemption to this where there is a requirement for a permanent presence, and care work will normally fall under these exemptions.
If you work with a colleague then it should be possible for you to take a break away from site because there will still be someone present who can tackle any care issues. If you are the only worker then your employer is entitled to tell you that you cannot leave the site.
Remember that the right is to one 20-minute unpaid break across the entirety of your shift, which will include any lunch break. If there is the requirement for a continuous presence then your employer can insist that you stay on site and cannot smoke.