I believe you would be able to extend onto the rear of the garage under permitted development provide you adhere to the rules which are basically the extension should extend out by more than three metres if an attached house or by four metres if a detached house. I do not know whether the Planners consider your house to be attached or detached! You will have to contact them for clarification. Should your plans involve extending beyond or higher than the rules permit you will need to get Planning Permission.
http://www.planningportal.gov.uk/england/public/buildingwork/projects/workcommonextensionreal/
If you wish to consider applying for planning permission, firstly, there are no guarantees with planning! One important factor in this kind of application is your neighbours 'right to light'. Can't really comment further as you've not indicated their house rear wall positions/glazing. Even if your current neighbour does not object the planners sometimes think about future purchasers rights. Mad but true.
The first thing I would do is check the online list of planning applications for your local authority and tap in your postcode. You'll be able to search for similar applications in your immediate area and get a feel for what is and is not accepted. Sometimes though if the houses in your street are all the same you can see that someone has done something similar already. You can also look out your window to see what others may have done.
Then book a meeting with a Planning Duty officer and try and gauge their opinion. Take a few photos along and your existing and proposed plans. You should get an idea as to whether its likely to be supported or not.
Ulitmately you'll just have to take the plunge and stick an application in. Nobody will be able to give you a guarantee despite what they might say!
If you do not think you require Planning Permission you are advised to gain a Certificate of Lawful Development.
Certificate of Lawfulness of Proposed Use or Development.
This is where you wish to confirm that what you are proposing would be lawful i.e. it would not require express planning permission. For example you may need to establish that what you have proposed does not constitute development, is ‘permitted development’, or already has planning permission.
What are the benefits of a Certificate of Lawful Development?
There are benefits in gaining a Certificate of Lawful Use or Development. It is a determination that has legal status providing certainty to prospective developers and purchasers of land and buildings. Certificates of Lawful Use or Development will be particularly beneficial to those participating in the housing market. Solicitors representing purchasers of, for example, extended dwellings, will usually require documentary evidence that extensions such as conservatories are lawful. This evidence may assist with the sale of property. Certificates of Lawful Use or Development also provide the necessary evidence that any works being undertaken are lawful if, for example, a neighbour were to make an enquiry or complaint about the work.
Basically, if you do not get a Certificate when you come to sell your house the buyers solicitor may ask for proof and you may have to apply for a cert in order to complete on the house sale (these take around 8 weeks BTW).
You will also need Building Regulations Approval as it is attached to your house albeit via your garage. Building Regs are a whole different kettle of fish to planning.
Have a read through the two links
Planning
http://www.planningportal.gov.uk/england/public/planning/applications/
and Building Regulations
http://www.planningportal.gov.uk/england/public/buildingregs/
