Just caught your post.
While there was significant flooding in some areas such as the Somerset Levels this has subsided and conditions are back to normal, other than some very specific areas. Travelling in July there should be no more problems than normal.
The Cotswolds and Wales are both good areas for cycling, but I must admit to being biased, living in South Wales.
The Cotswolds has very pretty towns and villages, very quaint "olde English" and some rolling hills. Wales has much more varied terrain. The coastal areas around Pembrokeshire/Preseli mountains; the beautiful mountains/reservoirs of the Brecon Beacons & mid-Wales, and probably the most scenic & challenging area of all - Snowdonia/north Wales with its lakes and mountains. Plus there are the castles. If mountain biking is your thing there are also many trail centres and off-road riding opportunities.
Accommodation is plentiful, and internet searches will find plenty of Guest Houses, B&Bs and small hotels, but book early as things tend to get busier from mid-July, when the schools close.
To reiterate, you will not have problems travelling due to last winter's floods, we're fully open for business again.