You most definitely do not need to buy a new bike. New wheels will transform a bike more than you would believe. Frames and wheels are the heart and soul of bikes. The rest is add-on frippery. Do some research, but £2-300 will buy you a decent set, spend more if you can and new wheels combined with (say) £30-40 road tyres and your entire bike will be transformed. Keep the old wheels/tyres combo for tracks and trails (which is what the Tricross was designed for) and the new wheels for the road. You now have two bikes. That being said - buying a cheapo Raleigh replacement wheel was a mistake.
Thanks for the advice.
I was broke and knew what I was buying with the Raleigh wheel - a cheap replacement which is enough for commuting.