From OPs explaination, if you won't explain how you got the money it'll be forfeited. That's the opposite of presumption of innocence.

I'm ok with having large amounts of cash with no obvious legitimate source triggering an investigation, but that's not what's happening.

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.