I am not an economist by profession
But, I'll have a go at this, thinking from first principles,
It depends whether we're talking about a worldwide legalisation of drugs, or legalisation of drugs in this country alone.
As each country would in fact have to legislate separately to legalise drugs, I'll consider the effects of legalising drugs in this country.
The thing is it's a totally different question if you think of the utterly unrealistic situation that the government just legalises drugs without trying to control their supply and sale.
My guess is that if a government in this country were to legalise all drugs, their motivation would be to raise some money from tax, and so they would be likely to try to keep the drugs sold at roughly the prices they are now. They might even grant themselves a monopoly on selling them. But more likely, they'd consult to find out how much it would cost to legally manufacture or grow the drugs, and then set the tax rates on manufactureres and growers, so as to to keep the price roughly as it is.
So all in all, probably, the effect would be we'd supply ourselves with drugs more efficiently, which would mean fewer people would make money out of it. Rather than a lot of people making a bit of money, you'd have just a few people making quite a lot of money, the consumers spending roughly the same amount of money, and the government making quite a lot of money.
The question then would be what the government did with the extra revenue.
They could use it to cut public borrowing, they could use it to cut taxes, they could use it to increase social security payments. They could even pay everyone a dividend. And clearly without numbers, this game all starts to get a bit vague
The other aspect to the whole thing, is that if drugs are now legal but heavily taxed, maybe there's still going to be money to be made from black-market drugs. Now the government's going to have a problem controlling this, if it completely deregulates the whole importing growing manufacturing thing, so my guess is they'd be more likely to grant licences. Which would mean you'd continue to have an illegal drugs market competing with the legit drugs market, if they could undercut them.
This is the problem with economics. It's not any kind of science, because they operate on totally incomplete information, and the scenarios they envisage never happen in some pure idealised fashion but always within a social and legal context.