I've carried out a vehicle data check on a car I intend buying in the UK. The check flagged up the fact that the vehicle had been written off by insurers last year. The category was D. The MOT is also valid and expires in May next year.  

My question is; will this fact affect my insurance quote and are there any other implications when I apply for insurance?

David I don't think it should effect your insurance premium, but bear in mind if you ever need to make a claim, about 15/20% is affected on the valued price, meaning you will be returned less had it not been damaged.

The fact that a vehicle has been written off should not necessarily put you off buying but it should make you check the current condition of the vehicle thouroughly. You should also bear in mind that the MOT may have been passed before the repairs were carried out. Some insurance companies will not insure vehicles where the owner knows it's been a write off so check this matter with your insurer before buying.