Hi Suzie, I'm a planning officer.
You will need planning permission if you require access off a classified road (A, B or C). Please be aware that some Council's have reclassified some roads since this legislation came in to make C roads where they anticipate problems with driveways, so ensure you check an up to date map. If your road is unclassified, it won't need planning permission in this respect.
You will also need planning permission if the area to be covered in hard standing is over 5 square metres and non-permeable. If you are using permeable paving or have suitable drainage within your site, no planning permission needed.
Householder planning applications are currently £150.
Even if you don't need planning permission, you will need to contact your Highways department to get permission for a dropped kerb, and either they or one of their approved contractors can carry out the work for you if they approve the application. I am not sure of the cost of the application or the works I'm afraid.
Hope this helps.