No, fitting private registration plates will not increase the cost of your car insurance.
This is because the installation of private plates is not considered to be a modification, as registration plates purely act as an identification number for your vehicle. Therefore, if you change your number plates after your insurance policy has already been enacted, you will simply be charged an administration fee by your insurer, rather than an increased cost in the premium itself.
If your private plate is particularly dear to you, you may wish to consider taking out ‘cherished number plate insurance’, which protects your investment in the event that your plates are lost or stolen.
If your vehicle does have modifications and you would like a competitive quote, visit our Modified Car Insurance page.