If you have a decent surge protector you should be ok, its more likley to be the person plugging and unplugging stuff that might be damaged.
If its still got an outdated consumer unit (doesnt meet current safety standards) gather up as much evidence as you can, tell your landlord its not safe and your wont be paying any rent until it is safe. Also ask for an independant electrician, not "one of the landlords mates", one of our old landlords did that with a plumber and an electrician, we got independants to come in after both and they both reported back to the letting agent the landlord was cutting corners with his tradesmen and the house wasnt safe...the letting company witheld the rent and had the work sorted.
Do you rent through a lettings/management company? or is it private?