Long-distance touring in single-engine airplanes is absolutely doable. I have done quite a few great trips in Europe, the US, Africa and Australia. All VFR.
That said, the further North you go, the trickier this gets. Weather being only one of the factors, especially in the UK the combo of weather and very restrictive airspace can put more than one spanner in the works.
IMHO, in northern Europe, any single-engine a/c should be considered a great way to travel - as long as you don't depend on it. Other than a short window in summer (and even that is dubious in the UK) you cannot rely on your machine to get you there - and back on the date / at the time you want it.
In short, to answer your Q:
Travel around Europe? Yes, definitely. As long as you are aware of the limitations.
In any case, good luck with your PPL and enjoy
