As a British full-time professional horse-player I can confirm that this is a complete nightmare, and a real risk to livelihoods and the whole industry.
Betting accounts are closed, often without warning, and only reopened once sufficient bank statements and at least three months' proof of income are provided. Income has to come from employment, and savings or gambling winnings don't count - a nightmare for the pro-gambler! Any large transactions visible on these statements need to be accounted for with corresponding statements provided from any linked accounts, even in some cases the statements of friends or family. Who wants to ask their parents to share their bank statements with William Hill just because they gave you £1000 as a wedding present?
I only have a few key accounts left, and now totally avoid any deposit into these for fear of triggering a review. If these accounts go, my only option will be to move out of the country or go back into employment for three months so I can demonstrate enough income to get some accounts reopened. Absurd!