Sure you can. It isn't always easy because traffic issues around, for example, Heathrow may cause London to have to descend you out of controlled airspace, you you may end up in IMC in class G without any radar service or rerouted with vectors instead of your flight plan. But that isn't exclusive to a C172 either. Typically to fly to the continent you'd be at FL080 to FL011 by filing at the lowest available levels. No one is going to ask you to climb to FL200. You'd be in airways (class A) in the UK / IFR only. unless you get dropped out into D or G. Elsewhere in Europe, in class E you'd be VFR/uncontrolled, mixing with IFR traffic which is controlled. ( hence the comments about "being on airways " in europe, but it isn't really).