What are the most effective exercises to improve stamina and speed on my cycle to/from work?
There's nothing bad about maintaining a steady pace but at some point you'll want to increase that pace. For a while you will be able to improve significantly by just informally "trying harder" and getting more skilled with the bike. After a while, however, you will plateau and it will seem like it is impossible to get much faster and you'll wonder how people on mapmyride (for example) can do the same route at unbelievable average speeds.

Of course it is possible to get much faster! And the most effective way to do it is with some type of regular interval training. This same concept applies to all endurance sports. The idea is that you have to push your exertion to at or above your lactate threshold to stimulate improvement. It is the aerobic analogy to lifting weights.

I am not going to attempt to lay out a program, but roughly it is going to be a series of efforts that last a couple of minutes with a few minutes of rest inbetween. During those intervals you really have to max out to get the benefit of the workout. A "real" interval workout is HARD and draining. It is not something that you'll want to do everyday.

Alternatively, just riding with fast group will do the same (albeit in a longer time) as guys tend to naturally compete and "put the hammer down" at every opportunity.