In which year were licensed betting shops allowed in england?

1963 i think! – This is the year the UK gaming and lotteries act was introduced.

However it was possible to bet using the Tote in 1928

“Since 1928, when it was established, the Tote has had an exclusive right to operate, or authorize others to operate, pool betting on horse races in Great Britain.

Pool betting is a particular form of betting where all the stakes are pooled, and the total pool is divided amongst the winners, less a deduction for the operator”

Source(s):

http://www.zaczebra.co.uk