Is here a such thing as a basic traveling allowance to the british to leave the uk to us

No, a british person is not required to establish BTA to travel to the US, that is probably a scam. But it is the other way around, a person travelling to the UK from the US requires a BTA which is only to ensure that the person can support himself while in the UK, understandable of course. It is a shame that the US doesn't initiate this, maybe they would not have as many homeless people living on everyone else.

How are they travelling, to relocate or on a tourist visa?

Canada now has this, and especially for immigraes, who have to establish that they have to at least have $60,000 or so to settle in Canada.