Oh, beautiful scenes in those photos already posted, but I have to admit I don't have "a" favourite area, because I like so many of them equally. The British Isles has probably the most varied landscape of anywhere in the world for their area; thanks to their extremely varied geology and temperate climate.
So places I like? A few in no special order, that I have seen:
The Dorset coast and Downs. Yorkshire Dales - including the Three Peaks area and the Eden Valley. Lune Valley leading to the Crook o' Lune, and the bend itself, in Lancashire. South Wales around the Brecon Beacons. Isle of Skye. Avon Valley upstream frpm Bath. Malvern Hills, Long Mynd and Wenlock Edge. Mendip Hills
And any number of small, individual spots in many places; from quiet woodlands to great wide vistas.
The R. Avon and the Royal Shakespeare Company Theatre, at Stratford-on-Avon:
Dry-stone walls and the church at Priddy, Somerset:
I used to visit the Dales a couple of times a year, and sometimes drove out that way from Ingleton to the M6 for my journey home.
I recall one day a few years ago learning that an 18-19C spot favoured by landscape painters had been re-discovered, and opened up again by the careful removal of trees that had grown since then and blocked the view. It is up on the river-cliff, facing up-valley from the Crook - I sought it out and walked up to it.
The Dorset coast around Worbarrow Bay, from the preserved paddle-steamer 'Waverley'. The original "Arish Mell" of my avatar photo and nick-name is the opening of the low, broad valley to the left:
