I do all my riding (commuting, day trips, club runs) on a steel framed Dawes Horizon touring bike with 28mm Continental GP 4 Seasons. It's a great bike and I've progressed loads since I've started riding in January (my average speed was around 11mph and now it's ~16mph), but I'm wondering if/when this bike will actually hinder me with regards to speed and efficiency.

I can keep up with the club runs in my local area (it's amusing when they're all on CF bikes and here's me on my steel tourer!), but I'll admit I struggle on steep hill climbs (10% and over). Is this something that having a racing bike with 23mm tyres and a lighter frame (my current build is around 12kg) will drastically help with, or will this just develop as I get fitter?

I'm not a professional, and don't need to spend $$$$ just to squeeze an extra 20 seconds on a climb, I'm just looking for sane advice on what kind of performance increase a road bike will entertain me with verses my current setup as I don't like the idea that I'd drop £800 on a decent road bike and end up with basically the same experience.