The authority should be able to give you an idea about the likely timetable. If it cannot decide your application within eight weeks, it should obtain your written consent to extend the period. If it has not done so, you can appeal to the Secretary of State. But appeals can take several months to decide and it may be quicker to reach agreement with the LPA. You can find out more about the appeals process in the planning section of the portal website.
If the local planning authority turns down an application or allows it, but only subject to conditions which the applicant finds unacceptable, the applicant can make an appeal and have the matter resolved by a Planning Inspector. An appeal is also permitted on the grounds of 'non-determination' when the local planning authority fails to determine the application within the statutory period. Very occasionally the Secretary of State will take the decision.
An appeal is, however, a last resort. Agreement can often be reached with the planning authority following discussion of the reasons given for the refusal and adjustment of the proposal.