Can I offer you some advice?
I did a Photographic Science degree at university (which was not a lot of use), I worked as an assistant to a wedding and portrait photographer for about 6 months. Later I worked in a large Photographic laboratory moving from the studio, to Rostrum camera and then photo-composition (which is taking 5 days to do what you can achieve in 5 mins in Photoshop nowadays)
I then moved into computer graphics and slide presentation production before starting my own design, conference and event company. We commission photographers and you need to realise that most photographers are self employed, they rely on their portfolio and their contacts to get work.
A photographer I work with a lot used to be on the local paper, then on the Times before moving to picture editor on the Telegraph. He is freelance and as he says he never knows where the next job is coming from.
If you want to make photography your career path then I would suggest you need to think "freelance" rather than "job". The best place to start would be as an assistant to a photographer however this will pay very badly, if at all. If you need to keep going with another job for the money then try and find something flexible that would allow you to work with a photographer part-time.
You will need to build your portfolio, research and develop clients yourself. Does the local restaurant or hotel need some new photography for their website or brochure, do they have a special event coming up, a new manager? Try approaching them and offering a trade, you do some pictures (good for both of you) and maybe get a free meal in exchange.
Try a local PR company, see if they have an event coming up. Often there is not a budget for photography and someone will take some snaps themselves, but if you turn in good work then you might be invited back and given a paying commission.
Is there a local band that wants some publicity pictures?
One thing to watch out for though, keep control of your copyright, be very careful to allow only limited use of your work. Consider offering a years free usage with a licence if they want to continue to use your work in the future.
Join the local camera club, talk to local photographers. As long as you don't steal the food out their mouths by undercutting them then they will often help guide you. Enter competitions both locally and nationally, winning one of these can really help you.
All of this will help you build a portfolio of work. The work should reflect what you are good at, if you can't really do portraits then don't include them, become a specialist if that's what works. I know another photographer who specialises in arial photography and planes because it was a subject he was really interested in and had a talent for.
Most commissions come from contacts, you have to build those relationships with people, start small and take your time, build trust with people.
As others have said though you have to know if this the type of career you are looking for.
My daughter has just started a Documentary photography degree and whilst I know she has a lot of talent I have a feeling I may be supporting her for a long time until she builds that network.
Working for myself is the best decision I ever made, scary at times but you feel more in control of your destiny.
Good luck!