Hey I am new to the site and also to road bikes.
I have a Rayleigh Pro Race bike and find the gear levers on the down tube a real pain and get an occasional wobble when changing gear.
Is it possible to have the levers mounted on the handle bars, if so how do I move them and what equipment do I need to get?
Yeah, I agree with GeorgeET. The downtube shifters are relatively easy to use, once you get used to them. I found that even with friction shifters I rarely misshifted, usually the chain will end up in some gear. Some people recommend trying to shift between gears as a learning experience. I found this to be harder than I thought.
I personally think that the shifters at the stem or on the flats of the drop bar are less comfortable to reach than downtube shifters.
Regarding integrated shift / brake levers for drop bars: There are good deals to be had for last- or before year's components. There are also still some mail order companies that have old 8 speed stuff. There are no integrated levers for less than 7 speeds (7 gears in the rear) as far as I know. You could try upgrading to 9 speed, but that will be expensive: new crank set, chain, cassette, rear wheel, shifters, dérailleurs, I guess in excess of 300 EUR.
Disclaimer: I did that. It made no sense financially plus the brakes are... different.