The cost of installing a patio varies mainly due to the quality of the slabs or paviers used the terrain on which it is to be laid.
It's always best to talk to your local planning office but generally, providing the patio at the rear of the house, there are no restrictions on the area of land which you can cover with hard surfaces at, or near, ground level. However, significant works of embanking or terracing to support a hard surface might need a planning application.
If you live in a listed building, you will need listed building consent for any significant works.
Usually you will not need building regulations approval but you must ensure that any works do not make access to your home more difficult by introducing steps where none existed before.
If you intend to undertake the work yourself you will need to take into account the cost of removing the spoil, even a 3m x 4m patio on a level site will produce over a cubice metre of spoil. Including the cost of sand and cement you could be looking at around £40 per square metre on top of the cost of the slabs.