Yeah I'd say it is possible, realistic even. But you'll need to be on the ball hitting new trends as they start, you'll need multiple income sources, and you'll need to automate a massive amount of design and marketing techniques.
Start off with small business web design - its a quick way to make cash but not too scaleable. Once you have that sussed, automate it. A job that took you 2 weeks for a couple of grand in the first 3 months should take you a day tops for the same amount of £, but ensure to keep the quality no less than 80% of the hand built sites. You're going to have to sell the product or get someone to sell it for you - door to door on small business and shops will get you 5 leads a day, with 1 job and a couple of good leads out of it - make sure you have your sales pipeline in place and efficient.
Another 3 months of automated client web design and you'll have a fair bit in the bank. Now sell all your customers a monthly product(SEO, hosting, whatever), what ever you can get out of them per month will be your wages for the next 6.
With the cash, and more importantly the knowledge, you have built up in the last 6 months, get some of your own sites out there. I'd buy established sites from Flippa personally, but if you have some good ideas build em from scratch.
Get it right and you'll hit the million between 10 and 12 months.
Questions you need top ask your self, if you want to do something like the above are:
Am I prepared to work 80 hour weeks on this?
Can I sell at this level of volume?
Can I learn, in 6 moths, how to automate 60% of your whole business?
I done similar when I started online, and I didn't hit the million. My priorities changed during it, and it was not as quick as I outlined above. But thats not to say you couldn't hit it mate
Jay