I have lived in England all my life.
It all depends on where abouts in England you are moving to.
I live in the northumberland, here there is alot of countryside so it is very pet friendly.
Maybe in London or furthur South might not be so pet friendly as they are busier cities.
True there are still lots of shops in the north, I usually take Poppy inside the shopping centres in her carrier and nobody has ever asked me to leave or anything like that.
But it may be different in other parts of the country.
So if you are moving to England I recommend the north.
The UK has been virtually rabies free for the past 100 years, so there are lots of policies in place when bringing an animal into the UK.
The good thing is that you dont have to put your pet in quarantine for 6 months before your trip anymore. But there will be paperwork.
Here is a useful link:
Pet Travel - Traveling With a Dog - Important Information Bringing the Family Pet on Vacation in the UK 