It’s entirely up to you, there are several firms doing dedicated EV tariffs, from Octopus to British Gas.
It’s pretty easy to work out the savings, if your mileage is mostly town then consumption will be something like 4miles per kw, if mostly countryside/motorway then 3-3.5 miles per kw. So, 5000 town miles at your standard tariff would cost you around £337 per year, the same miles on Octopus Intelligent Go would be around £93.
However, many of these deals also charge slightly more for the standard electric you use, so your standard use of 2723kw costs you £735 just now, but under Intelligent Go it would be £824 (all of these prices do not include your daily standing charge).
So your saving under Intelligent Go would be about £134 a year. More savings can be made if you load shifted some things like using your washing machine or dishwasher to the off peak times lots provided by the EV tariff.
Some EV tariffs only provide lower EV charging and do not offer off peak for everything else, OVO offer this, at 7p per kw. This would cost you £87.50 for your EV mileage, but I can’t see what their standard rate is when on this deal without doing a full quote…
As your mileage is low, there is not much difference between the deals on offer, but most should offer a decent saving against your overall bill vs staying on the standard rate.
In life, it's not who you know that's important, it's how your wife found out.