When comparing speed with your neighbour are you actually comparing like for like? Same ISP for example, wireless v ethernet connections. Wireless connections are usually slower than ethernet connections.
Have you carried out basic checks. Is your router plugged directly into your telephone socket rather than via an extension cable? Is there a filter? If you have telephone extensions in the house do they all have a filter?
Is the wiring in your house in good condition? If you have a BT phoneline have you tried unscrewing the bottom half of the box faceplate (if you have a new style box) and attaching your router/telephone (with a filter) directly into the BT test socket? This is perfectly legal and is one of the things that BT/your ISP will ask you to do for the basic checks. Usually if the speed increases and remains higher it points to the fact that you may have some suspect wiring.
If you still have an old type box you should consider having it replaced.