Where to do a week's tour in Britain?

The travel bug just hit with a vengeance! We just got the opportunity to travel for 10 days in late July and have decided to do a bike tour in Britain. Problem is, we have no idea where to go. A British friend suggested Scotland, another Brit thought that was a terrible idea and was more keen on Wales. We've only been to Dublin and the Heathrow airport, leaving us totally naive and open for opinions. Where do you suggest? Fitness isn't a problem. We are looking for what we deem "quintessential Britain"- castles, green rolling hills, thatched roofs, small roads, pubs...
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Devon/Corwall/Somerset/Wales/Yorkshire Dales/Yorkshire Moors/Peak District/Lake District/Northumberland/Scotland/North Downs/South Downs.
Castles-Scotland 100s of them.
Rolling hills-Devon/Cornwall/Yorks Dales/Moors/Peak District/Scottish Lowlands/Northumberland.
Thatched cottages-S/SW..Devon etc.
Mountains-Wales/Lake District/Scottish Highlands/Islands.
Flatlands-East Anglia/Lincolnshire/Yorkshire Wolds.
Pubs...it's Britain so everywhere.
My favourite 'British' tours have been Wales and SW Ireland, but I haven't toured Scotland. Loads of castles and hills in N Wales, beautiful coastline.
SW England will be very busy at that time due to school holidays.
You can string together the trip of a lifetime between three national parks - North Yorks Moors, Dales and Lake District. The Lakes might be busy that time of year but the ale, food, scenery and riding between the east and west coasts are sublime.
You don't know how lucky you are!
If the OP can watch the Tour de France Grand Depart this weekend to get an idea of what Yorkshire has to offer
Start in Edinburgh, a must see city, then the fantastic train ride to the Kyle of Lochalsh to the start of the cycle. End up in York, another city worth a look. This route would give you a good taste of the wide variety of geography and character of Britain.
It's a very Northern bias, but the South isn't worth the trouble if truth be told.