I encourage you to do it.
I bought my first house for cash following a similar approach. Basically I graduated in 1989 with zero debt (had scholarship and worked when I travelled in summer hols). By 1997 I had saved enough to buy a house for cash (140k) and also had quite a bit invested in investment trusts as a retirement fund. I was never stingy with things like holidays but was about things like eating and drinking out, buying expensive clothes and flash cars. I hated buying anything that lost significant value the moment I bought it. I rented a fairly basic 2 bedroom flat in that period but as I was working or out playing sport most of the time that was not an issue at all. I have no regrets, quite the reverse.
My rules of thumb were NEVER to pay for something unless I had earned the money for it first and to avoid all debt. I also saved my money mainly in investment trust monthly savings schemes, not cash. It takes a while for this approach to get going but if you stick with it you get into a virtuous circle whereby your savings are growing by a really significant amount every year. The regular savings takes the psychology out of it as well.
I was an avid reader of investment books (e.g. Jim Slater, Warren Buffet etc), the FT, ITS Online and Investors Chronicle in that period. I advise you to do that as well if you are investing the market rather than cash.
Good luck, your plan is good and you may reach your goal sooner than you expect.
