If you target the very wealthy, it's a very tiny burden to make them do paperwork to explain the origin of their money. In a situation like that, you can achieve due process without presumption of innocence.

This can be used for values over £50000, though.

That's probably not a great threshold, but for now I'm more worried about where it has been used than where it could theoretically be used.

The UK doesn't have a 5th Amendment.

Yeah, because they don't really have an actual consolidated constitution, but the presumption of innocence is one of the principles of English Common Law (see Woolmington v DPP), as well as being one of the rights in the Universal Declaration of Human Rights.

They just sneak past it by not actually sentencing you of a crime.

UK has parliamentary sovereignty, so any presumed common law right only exists until the Parliament passes a bill that effectively nullifies it.