As far as I am aware, dogs are allowed on public transport in England (at driver's discretion on buses).
The few times I had to use a bus (route 75) I have never encountered any problem.
On new year's day I was carrying a 10 week old terrier puppy and tried to board an almost empty bus on Perry Vale (route 356).
It was a sad scene I witnessed, as the fat driver spewed a "NO DOGS!!" scream.
Thank god for the screen around the driver's booth or the passenger boarding ahead of me would have been covered in his saliva.
No harm done. Walking keeps your body and mind healthy - an irony that would have certainly escaped this overweight driver.

Happy new year everyone