Although not technically a mountain, you could try a walk up kinder scout starting from hayfield in Derbyshire.
Start in Hayfield, go uo the summint of South head, (a big pointy hill), then cut across to Kinderscout.
The advantages of this are It is alot closer to you than north/south wales or the lakes, Becuse they are not that big, you can cover more ground in a day, and becayse of your lack of mountain experience, you will have less chance of getting into trouble.
Seriously though, dont under estimate even the likes of Kinder, There is a reason the Edale montain rescue team are called out everyday!
I agree with everyone else , that North wales would be your most ideal bet, as the mountains there are more mountain like. Im just thinking about travel time and expenses on your part.
Have fun!