Why doesn't the Government know how much they spend? Because they ask all the non-SME's they contract with to report on how much they spend with SME's on Government contracts.
As the larger suppliers don't run accounting software that differentiates between SME vs Non SME ( or carbon emissions or ethnic backgrounds or sexual persuasion) never mind between each individual sales contract, then it's a complete guessing game.
You know how much they buy, because you can get a report for that. After that it's guess work.
It would be better if the government first decided on a target that they could measure accurately. Directly awarded contracts. They can then measure it themselves. But they would mean they couldn't fudge the figures.
SME's are very important, but using an SME should be in context. Just because you engage an SME doesn't mean it's better. it often depends on the resource required and the value add given. It's a bit like setting a target to use small spanners in a garage. So less simple nonsense targets please and more smart objectives.