Yes, most garages can service an electric vehicle but, as many are still new and come with free servicing, you will probably use a manufacturer main dealer network. There are also some reputable specialist EV servicing companies, such as C who have a national mobile service.
It's important to note that most electric vehicles need very little maintenance and that servicing is very cost-effective as there are many less moving parts to maintain.
MOTs are very similar to ICE vehicles so your local MOT centre will be able to carry this mandatory test out (only applicable to cars over three years old).