Hi.
Britain is a great choice for a first tour. They speak English (I think!) and they are friendly. I've toured Britain many times and I've never needed a tour operator. It will probably double your costs and that means you can spend half the time there.
Now I will tell you July or August aren't the best times to visit anywhere except Antarctica. Three words; crowds, expense and booked.
If you are stuck with the dates, think about visiting a place less travelled. I've enjoyed many a quiet time on the north coast of Devon or Cornwall. There are also parts of Wales less travelled and I am not familiar with Ireland, but I understand they are rich these days, so that may or may not be a first choice.
I would think about riding along the tow path of a canal or on a rail trail for a more relaxed vacation. Although I tour totally unsupported I also credit card tour on a tandem with SWMBO.
I'm not sure of your interests, but CC touring can go like this: In the morning you awake at your B&B to a fabulous 'full English' breakfast of cereal, OJ, 3 eggs (any style), toast, jam, coffe or tea. After 'breakie' you hop on your bikes and do about 2 hours of touring until you arrive in the next town. There you buy supplies, and book the next B&B at the Tourist Information Centre (TIC). You have a relaxing lunch and bike for another couple of hours until you reach the B&B. You unpack and go out for supper at a pub and are back by about 11:00 for a full nights sleep.
You don't have to pay a tour company for that and you don't have to pay them for a route. In Britain and Northern Ireland use
Sustrans
Oh, one more thing. Although Europe appears small compared to the US (say), there are a lot of things to see and do. Don't try to do them all at once. Choose an area and spend your time there. Life is an experience, not a race. You don't have to finish first to win.
