Other answers have hinted at this, but it might not be obvious if you're not familiar with these things: the reason the rate is quoted as an AER not a monthly figure is due to compound interest.
Imagine the account did pay 1.5% per month. In the first month, it would pay £150 on your £10k, as you say; but in the second month, you would now have £10,150, so it would pay £152.25; on the third month, it would pay slightly more again, and so on.
This makes comparing accounts which pay out at different intervals difficult, because you can't just multiply the monthly figure by 12 to get the amount you'll earn over a year.
The AER is the "Annual Equivalent Rate", and represents the amount you will earn, including compound interest, if you leave money in for a year. So a 1.5% AER means either that the account pays exactly that amount at the end of the year, or it pays an equivalent amount spread throughout the year. However often it compounds, leaving £10000 in a 1.5% AER account for a year will gain you £150.
As others have said, the actual rate calculated each month will be slightly below one-twelth of 1.5% - the bank has calculated the rate to give an easy-to-read AER.
Another way to put it is that you will get on average £150 / 12 = £12.50 per month over the first year. The first month you will get less than that, and each month you'll get slightly more than the last because your balance will be slightly higher.