The main argument for any universal benefit is basically that it's cheaper to simply give the same benefit to everyone and then increase taxes than it is to administer a complex system to check people's eligibility for certain means-based benefits. In theory, if you give everyone 1500 quid, but then increase the income tax of people who earn above a certain amount by 1500 quid, then you can effectively give money only to the poor without needing a to have them prove their income with all of the admin that that entails. However, since tax is typically a race to the bottom, it's politically very difficult to do that.
It's worth mentioning that we already have benefits that aren't means tested. Child benefit, for example, is available to everyone regardless of income. Boris Johnson (or his various partners) can claim child benefit for all of his kids, although presumably that would involve actually acknowledging them.