Travelling by bicycle is in no way comparable to driving.

Of course, it's slower but You'll ride on small and sinuous roads through beautiful landscapes and villages. 
While carrying camping and some cooking stuff, You might swear on very steep ascents but You'll be free to stop whenever and wherever You want. Stoping for coffee, cakes, tea, photograph is a must then ad part of the trip concept! 

Starting at Newcastle-on-Tyne where the ferry from the continent berths, You'll follow the Tyne along Hadrian Wall to the city center. (A first stop must be done at "The Hub", a cycling café by the river).

Follow then Sustrans Reivers route to Kielder Forest where You'll cycle the only gravel and stone roads of the trip. The path along the Scottish Border is one of the most beautiful place ever.

After Carlisle, You can head to the Lake District National Park, enjoy the peaks and the ride down to the Irish Sea. From Workington, ride along the Solway Coast back to Carlisle and follow the the Hadrian Wall cycling path through Northumberland National Park.

This trip will take You through a variety of landscapes, on steep hills (though not very long)  and remote villages, in forests, cities and mountainous areas but most of all, will give You a lot of pleasures.