Should I get a 250cc motorcycle?

I've been riding on L-plates for almost a year now on my 125cc Honda. About ready to take my test and need to upgrade to a bigger bike. Hate being on a dual carriageway and not being able to overtake lorrys cos I can't get past 50mph. Was thinking about getting a ninja 250 but just worried it wont be powerful enough. Budget is an issue but don't want to buy something I'm not gonna be happy with. Will mainly be used for a 20mile commututerine but also going London-glasgow(400miles) a few times a year. Any advise please :)