The short answer? Yes, you can. The long answer? It depends on your tariff and energy provider.
Most  electric vehicle deals are only available to existing customers of that  company, but you may still be able to get one with a different provider  by jumping through some extra hoops.
If  you are already an existing customer, switching to a different EV tariff should be simple, as you can just call your provider up and they will  start the switching process for you.
However,  its worth knowing that to switch to an EV tariff you will need to have a  smart meter installed, if you haven't done so already. 
If you are not an existing customer, there are a few extra steps involved.
You  will need to switch to the energy provider first before you are able to  take up an EV contract. Make sure you opt for their cheapest energy  deal when you do, as it could take a number of weeks to make the switch.
Once  you've made the switch, you should be able to ask your provider to  begin the process of moving you to an EV tariff, but only after the  contracted start date.
However, many  providers are not taking on new customers at the moment, so it may be  difficult to switch. The situation changes regularly though, so it is  worth contacting your ideal provider to discuss the options for  switching.